Preheat oven to 400 degrees F (200 degrees C). Prepare 6 muffin cups with cooking spray.
Beat quinoa, eggs, feta cheese, mushrooms, onion, thyme, salt, and pepper together in a large bowl. Spoon into prepared muffin cups to about halfway full.
Bake in the preheated oven until edges brown and the tops are firm to the touch, 20 to 30 minutes.