1. Arrange oven rack 6 inches from the broiler. Preheat broiler to high.
2. Heat 2 teaspoons of the olive oil in an 8-inch, ovenproof, nonstick skillet over high heat. Add the mushrooms and cook, 2 minutes, stirring frequently. Reduce the heat to medium-high and add the asparagus. Cook in skillet for 2 minutes more.
3. While the mushrooms are cooking, whisk together the eggs, egg whites, chives, parsley, salt, pepper, and 1/4 cup of the cheese in a medium bowl. Add the remaining teaspoon oil to the pan, stirring the vegetables to coat. Pour the egg mixture over the mushrooms and asparagus and reduce heat to medium-low. Cook for 1 1/2 minutes, running a rubber spatula around the edges of the pan to keep the eggs from sticking.
4. Sprinkle the remaining 1/4 cup cheese over the egg mixture and broil it for 2 1/2–3 minutes or until frittata is golden brown and lightly puffed. Remove the frittata from the skillet, cut into 4 pieces, and serve it immediately.