Peel, core, and slice the apples into thin wedges. In a skillet, melt the butter over medium heat, then add brown sugar and cinnamon. Cook for 2-3 minutes until bubbly. Add apples, and cook until slightly softened. Spread them evenly in a greased 9-inch round cake pan.

In a large mixing bowl, combine flour, sugar, baking powder, and salt. In another bowl, whisk together eggs, milk, and vanilla extract. Gradually mix the wet ingredients into the dry ingredients until just combined.

Pour the batter over the apple mixture in the pan and spread it evenly. Bake at 350°F (175°C) for 30-35 minutes or until a toothpick inserted in the center comes out clean.

Allow the cake to cool in the pan for 10 minutes. Carefully invert the cake onto a serving plate, so the apples are on top. Serve warm or at room temperature.