CHAMETZ, Part IV: The Taste of Exile - Mishnah Pesachim 3:1

These are the types of grain with which a person fulfills their obligation [to eat matzah] on Passover: With wheat [hittim], with barley [se'orim], with spelt [kusmin], with rye [shifon], and with oats [shibbolet shu’al].

For possessing these one transgresses [the prohibitions of chametz] on Passover: Babylonian kutaḥ, [a dip with a sharp flavor that contains flour]; Persian beer; Edomite/Roman vinegar; Egyptian zeitom [a type of beer]; dyers’ broth [zoman]; bakers’ well-worked dough; and scribe's kolan. Rabbi Eliezer says: The same prohibition also applies to women’s adornments [i.e., cosmetics, that contain leaven].

This is the principle: any substance that is derived from a type of grain, one transgresses the prohibition of chametz on Passover.

Rabbi Shimon ben Lakish interpreted the second verse of the Torah with the various exiles.

"And the Earth was chaos" - that is Babylonian Exile, as it says. "I have seen the earth and behold, it is chaos!" (Jeremiah 4:23).

"and void" - that is the Persian Exile, as it says, "they scrambled to bring Haman [to the banquet]" (Esther 5:14).

"And darkness" - that is the Greek Exile, for they darkened the eyes of Israel with their decrees, and said them: Write on the horns of your cattle that you renounce the God of Israel!

"on the face of the deep." - that is the Exile of the Wicked Kingdom, whose end is unfathomable, like the deep.

Make of this a sacred anointing oil, a compound of ingredients, like the perfumer's recipe, to serve as sacred anointing oil.

Now we will explain the Mishnah of "through these one transgresses on Passover." (Mishnah Pesachim 3:1), that is, these things must be removed from the world: "Babylonian kutaḥ, Median beer, Edomite vinegar, Egyptian zitom, etc." This seems very strange, because if it is supposed to teach us that chametz in a mixture must be removed from the world, why do we need to consider all these examples? Wouldn't one or two suffice?

Therefore, it seems to me that the Mishnah is trying to teach us, with its precise language, that all of our redemptions came about on Passover. And so the future redemption will also be on Passover, and then all the husks [klippot] will be removed from the world.

Babylonian kutaḥ refers to the Babylonian exile. And it is known that Belshazzar was killed on Passover Eve. And with that all the klippot of Babylon were gone, and Israel then were then redeemed through Cyrus.

Median beer, if one adds up its gematria, comes to the same amount as: "Cursed is Haman, woe unto his sons!" For their downfall was on Passover.

These are the redemptions from Babylon and Media. But Greece is not included because their downfall was not on Passover.

After that comes Edomite vinegar, and if you add up all its letters [taking into account the tzaddi sofit which is 900] it comes to the same as "The annihilation of Sam-el, the guardian Angel of Edom," who will be annihilated from the world on Passover in the future....

And the Mishnah has placed the Egyptian exile at the end, for it is known that if the Egyptian exile had been 400 years as it was foretold in the Covenant Between the Pieces, then it would have been a complete redemption, and there would not have been any other exile. But because they were so immersed in the 49 gates of impurity, they could not have stayed there any longer without being corrupted beyond repair. So God, in God's mercy, took them out before their time. So all these other exiles are completions of the Egyptian exile. And that means that the Egyptian exile will not be over until the final redemption. And that is why we say that even in the days of the Messiah, we will still mention leaving Egypt, though our focus will have shifted to the oppressions of the ruling powers in those days.

Ben Zoma said to the Sages: Will the Exodus from Egypt be mentioned in the days of the Messiah? But doesn't it say: “Behold, days are coming, says the Lord, that they will no longer say: The Lord lives Who brought up the children of Israel out of the Land of Egypt. Rather: As the Lord lives, that brought up and led the seed of the house of Israel up out of the north country and from all the countries where I had driven them.” (Jeremiah 23:7–8).

They said to him that these verses do not mean that in the future the exodus from Egypt will be uprooted from its place. Rather, that the subjugation of the kingdoms will be primary and the Exodus from Egypt will be secondary.