Preheat oven to 400 degrees. Place the apple slices in a large bowl; set aside. In a small bowl, mix together the cornstarch, sugar, cinnamon, and nutmeg. Sprinkle the sugar mixture over the apples, tossing gently to coat.
Spread the mixture evenly into a 1 1/2 quart baking dish. In a separate bowl, mix the flour, brown sugar, salt, and butter until the mixture is crumbly. Add the sliced almonds and mix well. Spoon the mixture over the apples, pressing down slightly as you go. Completely cover the apples with the topping mixture.
Bake 45 minutes or until apples are tender. Remove from oven and cool on a wire rack to desired temperature for serving. Or after cooling, refrigerate until ready to eat and serve cold.