Heat 1 tablespoon of the olive oil in the nonstick skillet, then sauté the red onion over medium heat. Add all the spinach and cover with the lid. Allow to sweat until the spinach starts to shrink, about 5 minutes, then uncover and stir. Continue stirring until the spinach is all softened and limp, about 3 more minutes. Drain off any liquid and transfer the spinach mixture to the prepared casserole dish.
Heat the remaining olive oil in the skillet, and add the potatoes, zucchini, mushrooms, and bell pepper. Sauté over medium heat until all the vegetables have softened, about 5 to 7 minutes. Drain off any excess liquid.
In the large mixing bowl, whisk together the eggs, Feta cheese, milk, cottage cheese, parsley, salt, and pepper. Stir in the potato and zucchini mixture. Pour over the spinach in the casserole dish. Sprinkle sharp cheddar cheese all over the top, then lay the tomato slices on top of the cheese.
Bake in the preheated oven for 15 minutes. Reduce the heat to 350° F/175° C and continue baking until the casserole is lightly browned and just set, about 35 minutes. Remove from the oven and allow to cool about 5 minutes or so, then serve.
Remember to drain off any liquids before putting vegetables in the casserole dish, otherwise the quiche will turn out runny. The spinach and zucchini will be the most likely culprits.