To prepare ice cream, combine first 3 ingredients in a bowl; cover and freeze at least 3 hours.
To prepare crust, lightly spoon 2 cups flour into dry measuring cups, and level with a knife. Combine 2 cups flour, 3 tablespoons granulated sugar, baking powder, and 1/4 teaspoon salt in a food processor, and pulse 2 times or until blended. Add coconut and butter, and pulse 10 times or until mixture resembles coarse meal. Combine milk and egg yolks. Remove 1 tablespoon milk mixture; set aside. With processor on, slowly pour remaining milk mixture through food chute; pulse 5 times or just until blended. Press mixture gently into a 6-inch square on heavy-duty plastic wrap; cover with additional plastic wrap. Chill for at least 30 minutes. Roll dough, still covered, to a 14 x 10-inch rectangle.
Preheat oven to 350°.
To prepare filling, combine peaches, brown sugar, 6 tablespoons flour, nutmeg, and dash of salt in a large bowl; spoon into a 13- x 9-inch baking dish coated with cooking spray. Remove one sheet of plastic wrap from dough; place dough on peach mixture, pressing to edge of dish. Remove remaining sheet of plastic wrap; brush dough with reserved milk mixture. Cut 6 (2-inch) slits in dough; sprinkle with 1 tablespoon granulated sugar. Bake at 350° for 35 minutes or until golden. Let stand 30 minutes on a wire rack. Serve with ice cream.