Heat oven to 375°F.
Line a 9-inch pie plate with pie dough and place in freezer while you prepare quiche ingredients.
In a large skillet, heat olive oil over medium heat. Add asparagus spears and spinach. Cook until asparagus spears are slightly tender and spinach is wilted. Transfer spinach to a colander. Press firmly with back of a spoon to squeeze out as much liquid as possible. Set aside.
In a large bowl, whisk together eggs and milk. Stir in feta and mozzarella cheese. Season with salt and pepper, to taste.
Remove pie crust from freezer. Place asparagus pieces, spinach, and green onions on the bottom of the crust. Pour egg and cheese mixture over the vegetables and into the crust.
Bake quiche for 45 minutes or until quiche is set and slightly golden brown. Let quiche stand for 15 minutes before serving.
Approximate nutritional information, per serving (not including salt to taste):
370 calories, 23 g fat, 10 g saturated fat, 215 mg cholesterol, 500 mg sodium, 26 g carbohydrate, 2 g fiber, 6 g sugar, 17 g protein