Cookie Monster loves cookies. So what does a Jewish cookie monster do during Pesach, when cookies are Chametz?
Fortunately, Cookie Monster has addressed this very question at length.
Mem is for macaroon, or that what I believe Mem is for macaroon, or that what I believe Mem is for macaroon, or that what I believe Oh, macamaca Mem der ershter briv Me eat them on Pesach, when Chomez contraband It no make a difference if Streit’s or Geffen brand Me eat the cardboard canister, that not what makers planned Oh, macamaca Mem der ershter briv Me makpid on shiurim, just like the chocham ben Instead of two kezeitzim me gobble nine or ten But everything put in my mouth just spill back out again Oh, macamaca Mem der ershter briv To “all who are hungry” me happy to explain Me eat up all the macaroons but me still have some chrein Me soak them in the yayin, for they not made of grain Oh, macamaca Mem der ershter briv Me finish them by Chatzois, a little bit before On middle days of Pesach, me go back to the store And that way on the final days me still have plenty more Oh, macamaca Mem der ershter briv
The title "cookie" monster is really just a conveninece. In fact, his real name is the "Kof K" Monster and people take the letters kh and K and pronounce them as "cookie". So he eats whatever food is supervised by the Kof K, year-round.
Another theory has it that his name is actually the "K k'mon d'seter", as in "kosher, like the Mon which is hidden" so he eats things like Mon. And we all know that the food that can take on the flavor or form of anything that the eater wishes is tofu. So he is Sephardic.
See Shabbos 30b
עתידה ארץ ישראל שתוציא גלוסקאות וכלי מילת
When mashiach comes, Eretz Yisrael will grow cakes and clothes.
So let's say that Eretz Yisrael grows a cake on Pesach, is this chametz? If you say chametz is chametz because the dough fermented, this is not chametz. If you say chametz is chametz because it is chametz, then this is chametz.
This is lichorah a machlokess in the first mishna in Beitza
בֵּית שַׁמַּאי אוֹמְרִים: שְֹאוֹר בְּכַזַּיִת וְחָמֵץ בְּכַכּוֹתֶבֶת. וּבֵית הִלֵּל אוֹמְרִים: זֶה וָזֶה בְּכַזַּיִת.
According to Beis Shammai the leavening agent has a stricter halachah because it is the leavening that creates the cheftza of chametz. According to Beis Hillel is doesn't, because chametz is chametz regardless of how it was created.
Since the halachah will be like Beis Shammai when mashiach comes it turns out that chametz is only chametz when dough was leavened. Therefore if Eretz Yisrael grows cakes, you may eat them on Pesach.
Since the cookies that the Cookie Monster eats are spontaneously generated from the Cookie Tree this will also be permissible when mashiach comes, but in the meantime the Cookie Monster will have to starve.
There is an opinion amongst the later commentaries that the Cookie Monster was actually the Golem of Prague.
He only survived for one Pesach, after which he died (dramatically) due to chametz deprivation and argyria.
Some devout believers, await his return as the messiah...
In my house we frown on baking with matza products, and in general dislike "pesach versions" of recipes. Instead, Cookie Monster should look for recipes that never had hametz in them to begin with, such as almond-flour date-raspberry bars and flourless chocolate tortes.
If Cookie Monster eats kitniyot, there are also many peanut butter based recipes.
(Note: opinions vary on whether peanuts are permitted on Pesach; for example the OU says "In Europe different communities had different customs about peanuts. Some considered them to be kitniyot; while others ate peanuts on Passover.")