Heat the broiler to high. Set a rack in the upper third of the oven.
Put the eggs, cheese, pepper, and salt in a medium mixing bowl and stir together using a fork.
Heat a 10-inch nonstick, oven-safe pan over medium-high heat for about 3 minutes. When the pan is hot, add the butter and brush it around the surface of the pan. Add the asparagus and ham to the pan and sauté until heated through, about 3 minutes. Pour the egg mixture into the pan and stir with a silicone spatula. Cook until the egg mixture has set on the bottom and begins to set on top, 4 to 5 minutes. Sprinkle with parsley.
Place the pan under the broiler until lightly browned and puffy, 3 to 4 minutes. Remove the frittata from the pan and cut into 6 wedges. Serve immediately.