Preheat oven to 375°.
Combine rice and 1/2 cup feta cheese in a bowl, and press into a 10-inch quiche dish or pie plate coated with cooking spray. Steam zucchini slices, covered, for 5 minutes. Press zucchini gently between paper towels until barely moist. Combine zucchini, 1/2 cup feta cheese, salt, and pepper in a medium bowl, and arrange zucchini mixture evenly over rice. Combine mint flakes, nutmeg, and eggs, and stir well with a whisk. Pour over zucchini mixture. Bake at 375° for 40 minutes.