We are in Maseches Menachos, chapter 6, mishnah 3, which deals with the oil that goes into the preparation of the menachos. As we will see in the mishnah, a typical minchah goes through three stages of adding oil.
The three stages of adding oil:
Placing oil in the vessel: Oil is placed at the bottom of the service vessel, and the flour goes on top of it.
The mixing: More oil is added on top of the flour, and they are stirred and blended together.
The pouring: Once the minchah is ready, oil is poured over it from above.
The Rishonim disagree regarding a minchah that will be kneaded like a dough for frying in a pan or baking in an oven: is the water added first, or is the oil added first and only then mixed with the water?
In a minchah that is fried or baked there are additional stages. Baking is more involved, and we will return to it later in the mishnah. In frying - the machavas offering and the marcheshes offering - water is added, the dough is formed into loaves, and afterward they are crumbled: each loaf is folded in half twice and broken into thin pieces (the loaves are quite similar to pancakes), and the oil is placed on the crumbs.
The order of preparing the machavas and marcheshes offerings according to the Bartenura:
We will present only one approach, since there are fine differences among the Rishonim. The Bartenura follows the view of the Chachamim, and that is the halachah, and this order paves the way to see the picture of the mishnah as a whole.
Placing a little oil at the bottom of the service vessel.
Placing the fine flour into the service vessel on top of the oil.
Adding more oil onto the flour and mixing them together - this is the second placing of oil, and it comes before the water is introduced. In this the Bartenura follows the approach of the Rambam, while Rashi and Tosafos understand that the water comes before the second placing of oil.
Adding lukewarm water (at room temperature) and kneading everything together.
Dividing the dough into ten separate loaves.
Frying in a machavas or a marcheshes.
Folding into quarters and crumbling the loaves into pieces.
The third pouring of oil onto the crumbs.
Adding the levonah, and afterward the kemitzah.
This is the order for the machavas and the marcheshes. Later in the mishnah we will see that for those baked in an oven - the challos and the rekikin - there will not be three placings of oil.
The words of the mishnah:
"Kol hamenachos na'asos bichli" - any minchah whose entire preparation is done inside an earthenware vessel, and even if several vessels were used for it, requires three placings of oil, three separate additions that are three stages in the process:
"Yetzikah" - at the end, from above.
"Belilah" - in the middle, by mixing.
"Matan shemen bichli kodem la'asiyasan" - oil at the bottom of the vessel before the preparation begins.
It is puzzling that the Mishnah does not follow the chronological order, but instead opens with the last and closes with the first. The commentators noted this, and we have no fully satisfying answer.
The Mishnah's phrase "na'asos bikli" - that they are made in a vessel, meaning an earthenware vessel, comes to exclude what is baked in an oven, namely the loaves and the wafers that are baked in the oven. The Tanna here holds that the oven is not sanctified and is not an earthenware vessel, and therefore what is baked in it is not included in the three applications of oil. Those that are not baked in an oven require three pourings, while those that are baked require two smearings, and perhaps only one, as we will see in a dispute among the Rishonim.
The dispute between Rabbi and the Chachamim - when is the oil added:
"V'hachalos bolel, divrei Rabbi" - according to Rabbi, with the baked loaves one first bakes them, then breaks them into pieces, and only then mixes them with oil. According to the Rambam, in Rabbi's view this is the only time that oil is added, even though the halachah does not follow Rabbi.
"Vachachamim omrim: soles" - the Chachamim say that the oil is added to the fine flour, that is, to the flour of the dough, before the baking, unlike Rabbi who holds that it is added afterward. It emerges that according to the Chachamim, whose view is the halachah, at the time the loaves enter the oven the oil is already mixed into the dough.
Although the Mishnah speaks of loaves, the dispute between Rabbi and the Chachamim - whether the oil is added before the dough is broken into pieces (pesisin) or afterward - applies to the pan meal offering and the deep pan meal offering as well: according to Rabbi one prepares the dough without oil, and only afterward mixes the pieces with oil; and according to the Chachamim, which is the halachah, the oil is placed in the flour.
And regarding those baked in an oven: "HaChalos te'unos belilah" - the loaves are mixed with oil; "v'harekikin meshuchin" - the wafers are not mixed but are smeared with oil. This refers to what is done after the loaves or wafers have been prepared, at which point the oil is placed upon them. With items baked in an oven there is no placing of oil in the bottom of the vessel, and according to the Rambam the oil is placed in the dough itself; whereas with the wafers the oil is held back until afterward, and they are smeared on top.
"K'min chi" - the words of Rabbi Shimon:
How is the smearing performed on the wafers? The Mishnah says "k'min chi" - in the shape of the Greek letter chi. And it adds: "ush'ar hashemen ne'echal lakohanim" - the oil that remains after the smearing is eaten by the kohanim. It emerges that Rabbi Shimon says two separate things here: first, that the wafers are smeared with oil in the shape of a chi; and second, that oil remains and the kohanim eat it.
The Gemara brings two beraisos that disagree on both points:
The first: there is no need to smear in the shape of a chi; rather, one spreads the oil evenly over the surface of the wafer, like spreading butter on bread.
The second: one does not smear only once; rather, one goes back and smears oil again and again on those same wafers until no oil remains at all. The kohanim eat the oily wafers, and there is no separate oil left over to be eaten.
The halachah was decided in accordance with this view, and not like the wording of our Mishnah: one does not smear in the shape of a chi, but rather - according to the Rambam - one spreads the oil on the wafer and repeats the smearing until all the oil has been absorbed.
Three approaches to explaining "k'min chi":
Everyone agrees that a Greek letter is meant, and this is clear from the Gemara. But which letter is it?
The Rambam: The reference is to the Greek letter chi (written in English C-H-I, and sometimes X-I), whose shape is like an X, both in its capital and in its lowercase form. Since there is no X in the Hebrew alphabet, and smearing in the shape of an X is a simple and attractive way to spread the oil on the wafer, the Mishnah used the term of a Greek letter.
The Bartenura, who follows Rashi's approach: The reference is to a Greek letter whose shape resembles the Hebrew letter tes, something like a U - namely the letter epsilon, whose lowercase form is written like a U. This is somewhat puzzling: why do we need Greek letters when we have a tes, whose shape is roughly a U? One could answer that the tes is not exactly in the shape of a U, and when a genuine U or C shape was wanted, no Hebrew letter was available, so a Greek letter was needed.
And a further difficulty: why call an epsilon "chi"? One suggestion appears in ArtScroll's "Yad Avraham," and in square brackets - a sign that they had no source for it but were offering their own proposal, which seems convincing and resolves the question: "chi" means kaf, which is twenty in gematria, that is, like the twentieth letter; and indeed the twentieth letter of the Greek alphabet is epsilon.
The Aruch: The reference is neither to chi (X) nor to epsilon (U), but to lambda. The capital lambda is shaped like an upside down V. According to this it is understandable why a Greek letter was needed, since Hebrew has no letter shaped like a V; and as for why a lambda is called "chi" - just as the kaf is the eleventh letter of the Hebrew alphabet, so the eleventh letter of the Greek alphabet is lambda.
In any event, whatever the shape may be - X, V or U - all of this applies only according to Rabbi Shimon, and even that is not stated explicitly in the Mishnah; rather, it is the Gemara that attributes this view to Rabbi Shimon. And since this is not the halachah according to the Rambam, it is a side issue. The bottom line: the halachah is that one spreads the oil over the entire surface of the wafer, and continues spreading again and again until all the oil has been absorbed into those wafers.