In a medium skillet over medium-low heat, melt 8 tablespoons of unsalted butter, stirring frequently until it turns golden brown and fragrant, about 5-7 minutes. Remove from heat. In the same skillet, add your prepared 1.5-2 lbs of peeled and sliced Granny Smith apples along with 1 teaspoon of cinnamon. Cook for about 7-10 minutes until the apples are just softened, then set aside.

Preheat your oven to 350°F (175°C). While waiting for the oven to reach the desired temperature, grease a 9-inch round cake pan with butter or non-stick spray.

In a mixing bowl, whisk together 1 cup and 1 tablespoon of all-purpose flour, 1 teaspoon of baking powder, and ½ teaspoon of salt. In another bowl, combine the browned butter with ¼ cup + ¾ cup of dark brown sugar and ¾ cup of white sugar. Beat in 2 large eggs, ¼ cup of sour cream, and 2 teaspoons of vanilla extract until well blended.

In the same skillet used for the apples, combine the remaining 4 tablespoons of unsalted butter with ¾ cup of brown sugar over medium heat. Whisk until melted and smooth. Pour this mixture into your prepared cake pan, ensuring even coverage. Carefully arrange the cooked apple slices on top.

Pour the cake batter gently over the arranged apples in the cake pan. Place it in the preheated oven and bake for 35-40 minutes or until a toothpick inserted into the center comes out clean.

Once baked, remove the cake from the oven and allow it to cool in the pan for about 10-15 minutes. Run a knife around the edges to loosen the cake, then carefully invert it onto a serving plate.