Adjust oven rack to the lowest position and preheat oven to 350°F. Grease a 9-inch round, 2-inch deep cake pan and set aside. To create the topping, cut 2 apples into ¼-inch thick slices then cut remaining 2 apples into ½-inch thick slices. Set aside. In a 12-inch skillet, melt 4 tablespoons butter over medium-high heat. Add ½-inch thick apple slices and cook 4–6 minutes or until apples begin to caramelize, stirring occasionally. Do not fully cook apples. Add ¼-inch apples slices, ⅔ cup brown sugar and lemon juice and continue cooking 1 additional minute or until sugar dissolves completely and apples are well coated, stirring constantly. Transfer apple mixture to prepared cake pan and lightly press into even layer. Set aside while preparing cake. In a medium bowl, whisk together flour, cornmeal, baking powder and salt then set aside. In a large bowl, combine granulated sugar, remaining brown sugar and eggs, stirring to mix until thick and well incorporated. Slowly whisk in remaining butter until well combined. Add sour cream and vanilla, stirring to mix. Add flour mixture into egg mixture, whisking constantly until well incorporated and smooth. Pour batter into cake pan, spreading evenly over fruit topping. Bake 35–45 minutes or until golden brown and toothpick inserted into center comes out clean. Remove from oven and cool pan on wire rack 20 minutes. Run paring knife around sides of cake to loosen. Place wire rack over cake pan. Holding rack tightly, invert cake pan and wire rack together then carefully lift off cake pan. Place wire rack over baking sheet or large plate to catch any drippings. Remove any fruit that sticks to the bottom of the pan and position it on top of cake. Allow cake to cool completely before serving.