Preheat the oven and prep the baking dish - Preheat the oven to 375℉, convection bake setting. Generously butter the baking dish or spritz with a scant amount of oil.
Prep the veg - Sauté the spinach and mushrooms separately. Sprinkle the spinach with a bit of salt, and sauté until it wilts. Cool and squeeze out as much moisture as possible. Sprinkle the mushrooms with salt and sauté in a dry pan (no butter or oil). Sauté until the mushrooms soften and release their moisture, then continue cooking until the moisture evaporates.
Make the custard - In a large bowl, whisk together the eggs, flour, Parmesan, salt, pepper, garlic powder, and milk.
Fill the baking dish - Spread the spinach, mushrooms, and crumbled feta in the bottom of the dish. Pour the egg mixture over the veg mixture, and poke around with a fork to allow it to seep in and around the veg.
Bake and serve - Bake the quiche for about 35 minutes or until it's golden brown on top and the internal temperature reaches 160 degrees. Let rest briefly, then slice and serve.