Preheat the oven to 375.
Slice the onions, zucchini, and eggplant. In a large, deep oven-safe skillet (cast iron works well here), melt the butter over a medium-high heat. Add the vegetables and sauté until soft, about 8-10 minutes. When you put the vegetables in the pan will be very full. Don’t worry, they will shrink down as they cook.
While the vegetables cook, mix together the spices, cheeses, egg, and flour.
When the vegetables are ready, take the skillet off the heat and pour the egg mixture on top. Stir gently to make sure everything is covered in the mixture. Sprinkle a little extra mozzarella on top. Cover with a lid or aluminum foil and place in the oven.
Bake for 20 minutes, then remove the lid or foil and turn the oven to high broil and cook for another 5 minutes, or until the cheese on top is starting to bubble and brown. Serve hot, room temperature, or cold.