Preheat your oven to 350°F (175°C).

Grease a 9-inch round cake pan thoroughly with butter.

In a small saucepan over medium heat, melt the 4 tablespoons of butter for the topping, then stir in the brown sugar until it dissolves and forms a smooth caramel sauce.

Pour the caramel sauce evenly into the bottom of the prepared cake pan, then arrange the apple slices decoratively over the caramel.

In a medium bowl, whisk together flour, baking powder, and salt; set aside.

In a large bowl, cream the 1/2 cup softened butter with granulated sugar until light and fluffy, about 3-4 minutes.

Beat in the eggs one at a time, then stir in the vanilla extract.

Alternately add the dry ingredient mixture and milk to the creamed butter mixture, beginning and ending with the dry ingredients, mixing just until combined.

Carefully spoon the batter over the arranged apples in the cake pan, smoothing the top with a spatula.

Bake in the preheated oven for 40-45 minutes or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for about 10 minutes, then run a knife around the edges to loosen it.

Place a serving plate upside-down over the cake pan and carefully invert the cake onto the plate so the caramel and apples are on top.

Serve warm or at room temperature, optionally with a scoop of vanilla ice cream.