Preheat your oven to 350°F (175°C) and grease your baking dish to prevent sticking.
Spread the sliced apples evenly in the bottom of the baking dish, creating a colorful, layered base.
In a bowl, mix together the granulated sugar, cinnamon, and nutmeg, then sprinkle this fragrant mixture over the apples. This will help season and sweeten the fruit layer.
In a separate bowl, combine the flour, oats, and brown sugar, stirring to evenly distribute the ingredients.
Add the cold butter pieces to the dry mixture. Use your fingers or a pastry cutter to work the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumble topping evenly over the arranged apples, covering all the fruit with a thick layer of crumbly goodness.
Place the whole dish in the preheated oven and bake for about 40 minutes, or until the topping is golden brown and the apple filling is bubbling around the edges.
Remove from the oven and let it cool slightly, so the juices thicken a bit and the topping sets a little.
Serve warm, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream for extra comfort.
