Melt 3 tablespoons butter in 12" nonstick ovenproof skillet over medium heat. Add shallots; saute 2 minutes. Add prosciutto; saute until almost crisp, about 3 minutes. Add mushrooms, saute until brown and tender, about 6 minutes. Cool mushroom mixture in skillet 10 minutes.
Whisk eggs, 1 cup grated Fontina cheese, parsley, salt and pepper in large bowl. Stir in mushroom mixture. Melt 1 tablespoons butter in same skillet over medium heat. Pour egg mixture into skillet. Cook without stirring until bottom and sides are set (top will be undercooked), about 10 minutes.
Place skillet in oven and bake frittata until top is set, about 20 minutes.
Preheat broiler. Sprinkle frittata with remiaining 1 cup cheese. Broil until cheese melts, about 2 minutes. Using heatproof spatula, loosen frittata on all sides. Slide onto platter.
Can be made 2 hours ahead. Let stand at room temperature.