1. Preheat oven to 350°.
2. Cook fava beans in boiling water 30 seconds. Remove with a slotted spoon, and plunge beans into ice water; drain well. Peel tough skins from beans.
3. Place mushrooms in a small bowl of cold water; swirl mushrooms gently to remove any grit. Drain; rinse well. Drain on paper towels, patting mushrooms dry.
4. Heat oil in an 8-inch ovenproof skillet over medium-high heat. Add mushrooms to pan; sauté 5 minutes or until browned. Combine 1 tablespoon cheese, parsley, and next 6 ingredients (through egg whites) in a medium bowl; stir with a whisk. Stir in mushrooms and beans. Add egg mixture to pan; cook 1 minute, stirring gently. Place pan in oven; bake at 350° for 8 minutes or until edges are puffed and center is almost set. Remove from oven.
5. Preheat broiler.
6. Sprinkle top of frittata with remaining 1 tablespoon cheese. Broil 1 minute or until cheese melts. Garnish with fresh tarragon leaves, if desired.