Preheat the oven to 350 degrees F, and grease or spray a 13x9-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.
Notes
*After squeezing the moisture from the spinach (I find wringing it out in a clean tea towel to be most effective and efficient), you will have one big clump. Pull the pieces apart before adding to the egg mixture so the spinach is evenly distributed.
**I use canned artichokes in water, because I usually have them on hand. Frozen and thawed could be used, as could artichokes in olive oil that have been well drained. (The later would likely add a little extra flavor!)