Preheat oven to 350°F (175°C). Grease and line an 8×8-inch or 9-inch round cake pan with parchment paper.

1. In a medium bowl, whisk together flour, baking powder, salt, cinnamon, and nutmeg. Set aside.
2. In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy. Beat in eggs one at a time, then mix in vanilla extract.
3. Alternately add the dry ingredients and milk to the creamed mixture, mixing just until combined.
4. Fold in the chopped apples and pour the batter into the prepared pan, smoothing the top.
5. To make the crumble topping, mix flour, brown sugar, and cinnamon in a bowl. Add cold butter and mix with your fingers or a pastry cutter until crumbly. Stir in oats or nuts if using.
6. Sprinkle the crumble evenly over the batter.
7. Bake for 40–45 minutes, or until a toothpick inserted in the center comes out clean and the topping is golden.
8. Let cool for at least 15 minutes before slicing and serving.