Place the fresh or frozen peaches in a 2-quart square baking dish or 8x8x2-inch baking pan. In a medium bowl, stir together the brown sugar, oats, flour, cinnamon, and nutmeg. Using a pastry blender or two knives, cut in butter until mixture resembles coarse crumbs. Sprinkle over peaches.
Bake, uncovered, in a 375 degree F oven for 30 to 35 minutes or until fruit is tender and topping is golden. Cool.
To serve, layer peach crisp and ice cream in parfait glasses, beginning and ending with crisp. Top with whipped cream, if you like. Makes 8 servings.