• Preheat your oven to 350°F (175°C). Line a 9-inch round cake pan with parchment paper and set aside. I also greased the sides with some butter just to make sure the sides of the cake don't stick.
• In a medium saucepan, melt 1/3 cup of butter over medium heat. Stir in 1/2 cup brown sugar and 1/2 teaspoon cinnamon. Cook, stirring constantly, until the mixture starts to bubble and becomes smooth, about 2-3 minutes. Remove from heat.
• Pour the caramel mixture into the prepared cake pan, spreading it evenly across the bottom. Arrange the sliced apples in a single layer on top of the caramel, slightly overlapping if necessary. Let this set for a few minutes in the fridge while you prepare the cake batter.
• In a large mixing bowl, cream together 1/2 cup softened butter, 3/4 cup white sugar, and 1/4 cup brown sugar until light and fluffy. Beat in 2 eggs one at a time, then stir in 1 teaspoon vanilla extract.
• In a separate bowl, whisk together 1 1/2 cups flour, 1 1/2 teaspoons baking powder, 1 teaspoon cinnamon, and 1/2 teaspoon salt. Gradually add the dry ingredients to the butter mixture, mixing until just combined.
• Add the 1/3 cup milk to the batter. Again, mix until just combined.
• Gently scoop the cake batter over the arranged apples in the pan, smoothing it into an even layer. Bake in the preheated oven for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
• If you notice the edges of your cake getting a little too brown too fast, cover the edges with some aluminum foil (leaving the center of the cake exposed to the heat.)

For the Caramel Drizzle Sauce

• In a small saucepan, melt 5 tablespoons of butter over medium heat. Stir in 1/2 cup brown sugar and 5 tablespoons milk. Cook, stirring constantly, until the mixture comes to a boil and thickens slightly, about 2-3 minutes. Remove from heat and stir in 1/2 teaspoon vanilla extract.
• The sauce will thicken as it cools. If you find it too thick before you go to use it, just add a little bit of milk to it to thin it out.
• Allow the cake to cool in the pan for 15-20 minutes, then run a knife around the edges to loosen. Carefully invert the cake onto a serving plate. Let the cake cool completely before drizzling with the caramel sauce.