Preheat oven to 350°F (175°C).

Place 1/4 cup butter in a 9-inch round cake pan or springform pan and put it in the oven until melted.

Evenly sprinkle the melted butter with brown sugar.

Slice apples into 1/4-inch thick half circles (no need to peel). Arrange in overlapping concentric circles over the brown sugar in the pan.

In a large mixing bowl, combine flour, sugar, baking powder, cinnamon, and salt. Whisk to blend.

Add milk, melted butter, vanilla, and egg to the dry ingredients. Whisk until just combined.

Pour batter over the apple slices, spreading it evenly.

Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.

Run a knife around the edge of the pan. Allow the cake to cool completely before inverting onto a serving plate.