Preheat oven to 450 degrees, with rack set in top third. In a medium bowl, whisk together eggs, egg whites, and half the cheese; season with salt and pepper. In a medium cast-iron or nonstick ovenproof skillet, heat butter over medium. Add egg mixture; while it cooks, 1 to 2 minutes until edge is set, arrange apples on top in a circular pattern, starting from the outside edge, and sprinkle with remaining cheese.
Transfer skillet to oven. Bake until frittata is set in the center and cheese is browned, about 20 minutes. Using a rubber spatula, release frittata onto a cutting board; let rest 5 minutes. Cut into wedges, and serve.