Preheat the oven to 350 degrees and grease an 8x8 baking pan.
In a medium bowl, mix the diced apples with cinnamon and nutmeg. Set aside.
In another bowl, combine 1/2 cup flour, the oats, brown sugar, and 2 tablespoons butter. Rub the mixture together until it forms coarse crumbs for the topping.
In a large bowl, beat the remaining 2 tablespoons butter with the granulated sugar until light. Add the egg and mix well.
Stir in the baking powder, salt, and remaining 1/4 cup flour. Alternate adding the milk until a smooth batter forms.
Spread the batter into the prepared pan. Layer the spiced apples on top, then drizzle with half the caramel sauce.
Sprinkle the crumble mixture evenly over the apples.
Bake for 35 to 40 minutes until the topping is golden and a toothpick inserted in the center comes out clean.
Cool slightly, then drizzle the remaining caramel sauce over the cake before serving.