Spray an 8- or 9-inch round cake pan with nonstick spray.

Combine butter and brown sugar for topping in a small saucepan over medium heat. Cook, stirring occasionally, until butter has melted and mixture begins to simmer gently, 3 to 4 minutes. Don't let the caramel mixture come to a boil; just allow it to bubble gently for a couple of minutes so it can thicken slightly.

Pour into the prepared cake pan, then arrange apple slices all around the pan as desired. Place in the refrigerator so the topping can set while you prepare the cake.

Preheat the oven to 350 degrees F (175 degrees C). Whisk flour, cinnamon, baking powder, and salt together in a bowl.

Beat butter, sugar, and brown sugar in a separate bowl with an electric mixer until light in color and fluffy, 2 to 3 minutes, scraping down the bottom and sides as needed. Blend in eggs, incorporating slowly and scraping down the sides again, as needed. Mix in vanilla. Add in dry ingredients on low speed, blending just until combined; batter will be thick.

Remove the cake pan from the refrigerator. Gently spread the thick batter over the topping, trying not to disturb the apples too much.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 40 to 45 minutes. Remove from the oven and set on a cooling rack for 15 minutes.