Preheat oven to 400 degrees F (200 degrees C). Lightly grease a 10-inch square baking dish and line it with parchment paper.
Place the pumpkin in a microwave-safe bowl; cover and cook in microwave on full power, stirring halfway through cooking time, until tender, about 5 minutes. Place the potato in a microwave-safe bowl; cover and cook in microwave on full power until tender enough to pierce with a fork, about 4 minutes.
Combine the pumpkin and potato in a large bowl. Add the spinach, feta cheese, Cheddar cheese, and eggs; stir. Transfer mixture to prepared dish; top with sliced onion.
Bake in preheated oven until firm, about 25 minutes. Allow to rest 5 minutes before serving.