Mushroom and Fontina Quiche

Name: Mushroom and Fontina Quiche
Ingredients: 1 refrigerated pie crust (half of 15-ounce package); 2 tablespoons (1/4 stick) butter; 2/3 cup chopped shallots (about 3 medium); 5 cups sliced assorted mushrooms (such as chanterelle, stemmed shiitake, oyster, crimini, and button; 12 to 14 ounces), large mushrooms halved; 4 large eggs; 2/3 cup half and half; 1/3 cup whole milk; 1/2 teaspoon salt; 1/2 teaspoon freshly ground black pepper; 1/2 teaspoon freshly grated or ground nutmeg; 1 1/2 cups (packed) coarsely grated Fontina cheese (about 7 ounces), divided