Preheat the oven to 350°F (175°C). Butter a 9-inch round cake pan.
In a small saucepan, melt 3 tablespoons of butter and brown sugar over low heat until combined. Pour the mixture into the cake pan and arrange the apple slices on top.
Whisk together flour, baking powder, and salt. In another bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in eggs, one at a time, and mix in vanilla extract.
Gradually add the dry ingredients to the creamed mixture, alternating with milk. Mix until just combined and pour batter over apple layer.
Bake in preheated oven for 40 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes, then carefully invert onto a serving plate. Serve warm.
Notes
Enjoy this cake warm or at room temperature with a scoop of vanilla ice cream or a dollop of whipped cream.