Preheat oven to 350° F. Grease a 9-inch round cake pan generously with cooking spray or softened butter to prevent sticking. For extra assurance, line the bottom of the pan with a round of parchment paper cut to fit. Set the prepared pan aside.

In a medium mixing bowl, whisk together the flour, baking powder, salt, cinnamon, and nutmeg until the dry ingredients are fully combined and evenly distributed. Set aside.

In a large mixing bowl, combine the melted butter, granulated sugar, and brown sugar. Whisk vigorously until the mixture is smooth and well incorporated. Add the eggs and vanilla extract, and whisk again until the mixture is creamy and fully combined.

Pour the dry ingredients into the bowl with the wet ingredients. Using a rubber spatula, gently fold the dry mixture into the wet until just combined. Be careful not to over-mix. Add the chopped apples and fold them in evenly. The batter will be quite thick and it may seem like there are too many apples, but that’s what gives the cake its moist texture and fruity flavor.

Transfer the batter into the prepared cake pan and use the spatula to spread it out into an even layer, making sure it reaches all the way to the edges.

Bake for 28–32 minutes, or until a toothpick or cake tester inserted into the center of the cake comes out clean with just a few moist crumbs attached.

Allow the cake to cool in the pan on a wire rack for about 20 minutes. Then, run a dull knife or small offset spatula gently around the edges of the cake to loosen it from the sides of the pan. Invert the cake onto a plate, carefully peel off the parchment paper from the bottom, and then invert it again onto a cooling rack so the cake is right side up.

Serve the apple cake warm, when it’s soft and comforting, or let it cool completely and enjoy at room temperature.