Prepare the Caramel:

In a medium saucepan, melt 1 cup of sugar and 1/4 cup of butter over medium heat, stirring until dissolved. Cook until it turns a deep amber color (about 5-7 minutes).

Remove from heat and carefully add 1/4 cup heavy cream, 1/2 teaspoon vanilla, and a pinch of salt. Stir until smooth.

Arrange Apples:

Pour the caramel into a greased 9-inch round cake pan. Arrange the apple slices on top of the caramel, overlapping them slightly.

Make the Cake Batter:

In a bowl, whisk together 1 1/2 cups flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt.

In another bowl, cream 1/2 cup softened butter with 1 cup sugar until fluffy. Add 2 eggs and 1 teaspoon vanilla, mixing well.

Gradually incorporate the dry ingredients and 1/2 cup sour cream, mixing until just combined.

Bake:

Pour the batter over the arranged apples and caramel. Bake in a preheated oven at 350°F (175°C) for 35-40 minutes or until a toothpick comes out clean.

Cool and Serve:

Let the cake cool in the pan for 10-15 minutes before inverting onto a serving plate. Serve warm, optionally with ice cream or whipped cream.