Prepare your baking essentials. Preheat your oven to 350°F (175°C). Grease and flour a 9-inch springform pan, or line with parchment paper for easy removal.
Mix the dry ingredients. In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
Prepare the apples. Peel, core, and dice the apples into roughly 1/2-inch cubes. Toss them with a tablespoon of flour to prevent sinking during baking.
Cream the butter and sugar. In a large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy, about 3-4 minutes. Don’t rush this step—proper creaming creates air pockets for a tender cake.
Add the eggs and vanilla. Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract until just combined.
Incorporate dry ingredients and sour cream. Add the flour mixture to the butter mixture in three portions, alternating with the sour cream, beginning and ending with the flour. Mix on low speed just until combined—overmixing will result in a tough cake.
Fold in the apples. Using a rubber spatula, gently fold the diced apples into the batter until evenly distributed.
Make the streusel topping. In a small bowl, combine brown sugar, flour, and cinnamon. Cut in the cold butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs. Stir in nuts if using.
Assemble and bake. Pour the batter into the prepared pan, smoothing the top with a spatula. Sprinkle the streusel topping evenly over the batter. Bake for 45-50 minutes, or until a toothpick inserted in the center comes out clean with a few moist crumbs.
Cool before serving. Allow the cake to cool in the pan for 15 minutes, then remove the sides of the springform pan and let cool completely on a wire rack. For warm serving, wait at least 30 minutes before cutting.