Preheat oven: Preheat your oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan or line it with parchment paper.
Mix dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
Cream butter and sugars: In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar together until light and fluffy—about 2–3 minutes with an electric mixer.
Add eggs and vanilla: Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Incorporate sour cream: Mix in the sour cream (or Greek yogurt) until smooth and well combined.
Combine wet and dry: Gradually add the dry ingredient mixture to the wet ingredients. Stir until just combined—do not overmix.
Fold in apples: Gently fold the chopped apples into the batter, making sure they are evenly distributed.
Bake: Pour the batter into the prepared pan and smooth the top. Bake for 40–45 minutes, or until a toothpick inserted into the center comes out clean.
Cool and serve: Let the cake cool in the pan for 15–20 minutes before slicing and serving. Serve warm or at room temperature.
