Preheat grill for searing. Preheat oven 450F.
Wash, dry, cut off the stems, and slice eggplants and zucchini 1/3" thin alongside. Spray or brush them with olive oil and season with salt and pepper.
Prepare two half-size baking sheets and two silicone mats. Wash, dry, peel, and slice potatoes 1/8" thin alongside. Arrange overlapping layers of potatoes on a baking sheet lined with a silicone mat, spray them with olive oil, season with salt and pepper, cover with another silicone mat, and place the second baking sheet on top. Bake for 30 minutes.
Meanwhile, grill sliced eggplants and zucchini.
Start making the bechamel. Burn half an onion over an open fire. In a saute pan, melt butter, add flour, cook stirring until it smells like cookie dough, whisk in 1 cup of milk, add the rest of the milk whisking, add all seasons, and cook over low heat for about 15 minutes stirring from time to time. Strain it through the sieve and discard solids when done.
Meanwhile, peel and dice an onion. Peel and chop garlic. Strain and dice bell peppers. Strain garbanzo beans. Open cans with tomato puree and diced tomatoes. In a saute pan, heat 1 tbsp of olive oil and saute onions. Add peppers and diced tomatoes and cook stirring for 1-2 minutes. Add garlic, herbs, and garbanzo beans, season and simmer over low heat until most of the liquid is evaporated. Check the seasoning and adjust if needed.
Assemble the casserole. Start with lining the quarter-size deep pan with half of the eggplant slices.
Next, arrange a layer half of the zucchini slices.
Evenly spread tomato, bell pepper, and garbanzo beans layer. Sprinkle the top with crumbled Feta cheese.
Carefully transfer half of the overlapping potatoes to cover the red layer.
Repeat zucchini and eggplant layers to finish with the second half of potatoes and bechamel. Sprinkle with grated parmesan, arrange artichoke hearts and bake in the preheated 400F oven until the top layer is slightly caramelized, for about an hour. Timing depends on the initial temperature of the layered vegetables and sauces.
All layers of this casserole are cooked before the assembled dish goes to the oven, so we are only heating them all through to let the individual flavors like single notes to combine into a song. After that, the dish can be served hot, or you can let it cool down to the room temperature and then set for a few hours in a refrigerator to make portioning easier. To serve a small number of portions, reheat in a microwave. Otherwise, heat in the 350F oven, covered with foil to prevent overdrying.