Preheat your oven to 350°F (175°C). Grease and flour a 9-inch springform pan or line it with parchment paper for easier removal.
In a mixing bowl, whisk together the flour, baking powder, baking soda, ground cinnamon, nutmeg (if using), and salt. Set aside.
In another bowl, cream together the softened butter and granulated sugar until light and fluffy using a hand or stand mixer.
Add the eggs one at a time to the butter and sugar mixture, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Fold in the diced apples gently with a rubber spatula until evenly distributed throughout the batter.
Pour the batter into the prepared springform pan and spread it evenly.
In a small bowl, mix the brown sugar and ground cinnamon together for the topping. Sprinkle this mixture evenly over the top of the batter.
Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before removing the sides of the springform pan. Let it cool completely on a wire rack before slicing.