Preheat oven to 350°F Season the eggplant lightly with salt and pepper and dust it with a bit of flour. Place it on a flat baking sheet and bake until browned, about 15 minute (You will need to do this in batches).
(Have a wide bowl filled with ice water ready and set aside). In a large pot of boiling salted water, blanch the zucchini, squash and potatoes 2-3 minutes until slightly tender. Remove them with a slotted spoon and place immidiately into the ice water. then place on a rack to dry.
ASSEMBLY: Grease a 9x13 baking pan and sprinkle with breadcrumbs. Carefully layer the bottom first with the eggplant evenly across filling all the gaps. Sprinkle lightly with the feta and parmesan cheeses, then a few sliced red peppers. Season with salt, black peper, and italian seasoning.
Add the potato slices in an opposite order, then layer squash and zucchini in same fashion. re-seasoning in between layers and finish with final layer of eggplant. Set aside.
BECHAMEL: In a small bowl beat eggs and hot sauce and set aside. Melt the butter in a saucepan. Whisk in flour, salt, and pepper, and cook about 1 minute or until it binds, stirring constantly.
Gradually whisk in the cream and cook, stirring constantly, over medium heat until thick and bubbly.
Add reserved eggs to sauce mixture, mixing well. Add parmesan cheese, and stir to blend.
Spread the béchamel over the top of the vegetables. Bake for 40-45 minutes, until béchamel is golden on top. Remove from oven and let it rest for 5-10 mins before serving.