Preheat the oven to 350°F (175°C).

Grease a 9-inch round cake pan.

In a small saucepan, melt the butter for the topping over medium heat.

Stir in the brown sugar, cinnamon, and nutmeg until smooth.

Pour the caramel mixture into the prepared cake pan.

Arrange the apple slices evenly over the caramel layer.

In a medium bowl, whisk together the flour, baking powder, salt, and cinnamon.

In a large bowl, beat the softened butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition.

Mix in the vanilla extract.

Add the dry ingredients alternately with the milk, beginning and ending with the dry ingredients.

Spread the batter evenly over the apples.

Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.

Cool in the pan for 10 minutes.

Carefully invert the cake onto a serving plate.

Allow the caramel topping to settle before serving.