Preheat the oven to 350 degrees F, and grease or spray a 13×9-inch baking dish.
In a large bowl, whisk together the eggs, yogurt, salt, pepper, garlic powder, and red pepper flakes. Stir in the spinach, artichoke hearts, and 3/4 cup of both cheeses. (You can eyeball the cheese; you just want about 1/4 cup each reserved for topping.)
Pour into the prepared pan. Sprinkle with the remaining Parmesan and mozzarella.
Bake 30 minutes, give or take a few depending on oven, or until the eggs are just firm in the center and the edges are lightly golden.