Beat eggs, milk, salt and pepper in a medium-size bowl until blended.
Stir in 1/2 cup cheese. Set aside.
Melt butter in a 10-inch nonstick skillet with ovenproof handle over medium heat. Add mushrooms, shallots and asparagus. Cook and stir 3 minutes until vegetables are crisp, yet tender.
Reduce heat to medium and pour egg mixture over vegetables. Cover and cook 10 minutes, or until bottom of frittata is set, carefully lifting edge with spatula and tilting skillet as necessary to allow uncooked portion to flow underneath.
Place skillet under broiler. Broil 2 minutes or until top is set but not brown.
Top with remaining 1/2 cup cheese. Let stand until cheese has melted.