PREP THE BAKING PAN Using a 9" non-stick cake pan that's at least 2" tall on sides, grease and line the pan with a parchment paper round on the bottom, then grease it again on top of the parchment paper with more butter and a light sprinkling of flour. Tap any excess flour out of the pan.
Heat oven to 350 degrees and adjust rack to lowest position.
MAKE THE APPLE MIXTURE
Slice the peeled apples in half from the stem to the bottom, Cut two of the apples into 1/4" thick pieces, set these aside in a medium-sized bowl. Cut the remaining apples in 1/2" thick slices as evenly as possible. Melt the 4 tablespoons of butter in a medium non-stick skillet on medium-high heat. Add the 1/2" thick slices first into the pan with melted butter, and stir a couple of times to coat. Let these heat for about 5 minutes until they begin to caramelize, carefully stirring a couple of times, making sure they don't fully cook.
Add the rest of the apples to the skillet and combine, cooking for another minute.
Place the cooked apples in the bottom of the prepared cake pan, and use the back of a spatula to evenly press them down into one layer.
MAKE THE CAKE
Whisk the flour, baking powder, and salt together in a medium bowl
In another large bowl, whisk the sugar, brown sugar and eggs together until thick and combined.
Slowly whisk in the cooled melted butter and then add the sour cream and vanilla and continue to mix just until combined.
Add the flour mixture, mixing just until combined and then pour it over the apples in the cake pan.
Bake until golden brown, about 35-40 minutes, until a toothpick will come out clean when poked and removed from the middle of the cake
Remove cake from the oven and place on a wire rack for 20 minutes, then use a sharp knife to go around the edges to loosen the cake from the pan
Using a cake plate or platter, invert the cake and pan together, lifting the cake pan off the right-side up platter to catch any drips
If any of the apple pieces stay stuck in the pan or fall off, just position them on top of the cake with a fork (or your fingers:))
Cool another 20 minutes and serve with whipped cream if you like.