Preheat your oven to 350°F (175°C).

In a large mixing bowl, toss your sliced firm apples with brown sugar, vanilla extract, lemon juice, and ground nutmeg. Let sit for about 15 minutes.

Cream together the softened butter and granulated sugar until light and fluffy, about 4-5 minutes. Add eggs one at a time, ensuring each is fully incorporated.

In a separate bowl, whisk together the all-purpose flour, baking powder, ground cinnamon, and salt until combined.

Gradually add the dry ingredients to the creamed butter and sugar, alternating with the milk, and mix until just combined.

Grease a 9x13-inch baking dish. Pour half of the cake batter into the dish, layer the apple filling, and then spread the remaining batter on top. Bake for 45-50 minutes until golden brown.

Allow to cool for 10-15 minutes before transferring to a wire rack.