One reason the first Passover feels archaic to modern readers is that it was archaic even to the people eating it. Targum Pseudo-Jonathan on Exodus 12:9 piles up the restrictions: do not eat it raw, do not boil it in wine or oil or any other fluid, do not cook it in water. Roast it over fire, with its head, its feet, and its inward parts all there on the spit.
This is not how Egyptians cooked meat. Egyptian cuisine boiled and braised. The Pesach offering had to refuse all of those techniques. The lamb is cooked whole, on an open flame, in a way that leaves no margin for disguise or elaboration. No sauce, no broth, no layering of flavors. Just fire and meat.
The rabbis read this as the meal of people who have no time. Boiling takes hours and a pot large enough to hold the bird. Roasting over fire is faster and requires only a spit. Israel was about to leave, and the meal was designed to be eaten at the speed of a departure.
The inclusion of the head, feet, and inwards is more theological than practical. The whole animal must be present on the plate because the whole sacrifice was being offered. To eat only the choice cuts would turn Pesach into a dinner. Eating the whole creature made it a rite.
Takeaway: The first Passover was not a menu — it was a refusal. Every Egyptian cooking technique was rejected, in order to break the habits of slavery at the table.