Prepare Sweet Potatoes: Peel the sweet potatoes and trim off the ends. Use a mandoline slicer to cut the sweet potatoes into thin, even rounds.
Prepare the Pie Dish: Coat the pie dish evenly with cooking spray. Arrange overlapping sweet potato rounds across the bottom of the dish.
Build the Crust: Cut some of the sweet potato rounds in half. Arrange the half-rounds around the sides of the pie dish, overlapping them slightly to form the edge of the crust.
Bake the Crust: Bake the sweet potato crust at 350°F for 20 minutes.
Heat the Oil: While the crust bakes, add 1 teaspoon oil to a skillet and heat it over medium heat.
Cook the Onion: Add the sliced onion to the skillet and cook over medium heat for about 4 to 5 minutes, stirring occasionally, until softened.
Wilt the Spinach: Add the baby spinach to the skillet. Cook for about 2 to 3 minutes, stirring frequently, until the spinach is wilted and combined with the onion.
Start the Egg Mixture: Pour the milk into a large mixing bowl. Add the kosher salt and red pepper.
Add the Eggs: Add the 4 large eggs, black pepper, and 2 egg whites to the bowl.
Whisk the Filling: Whisk the milk, eggs, egg whites, and seasonings together until evenly combined.
Increase the Oven Temperature: After removing the baked sweet potato crust from the oven, increase the oven temperature to 375°F.
Fill the Crust: Spoon the cooked onion and spinach mixture evenly into the sweet potato crust.
Add the Egg Mixture: Pour the egg mixture evenly over the spinach and onion filling.
Add the Feta: Sprinkle the crumbled feta cheese evenly over the top.
Bake the Quiche: Bake at 375°F for 35 minutes, or until the egg filling is set and the top is lightly browned.
Slice and Serve: Let the quiche settle briefly after baking, then cut it into wedges and serve.