Preheat oven to 450° and grease a large baking sheet with cooking spray.
Separate egg whites and yolks, placing egg whites in a large bowl and yolks (careful not to break them!) in a separate bowl.
Add cream of tartar to egg whites and beat until stiff peaks form, 3 minutes. Gently fold in Parmesan and season with salt and pepper.
Spoon 8 scoops of egg whites to prepared baking sheet and indent centers to form nests. Bake until lightly golden, about 3 minutes.
Carefully spoon 1 egg yolk into center of each nest and season with salt and pepper. Bake until yolks are just set, about 3 minutes more.
Sprinkle with pepper. Serve immediately!