Position a rack in the center of the oven and preheat to 375º.
Peel the apples and cut them off the core into 6 equal pieces. Melt one stick of butter in a well-seasoned 10" cast iron or other oven-proof skillet. Sprinkle the granulated sugar over and stir to distribute evenly. Lay the apples, rounded side down, over the sea of buttery sugar, placing them snugly next to one another. You should have about one apple left over. Chop that up fairly finely and set aside. Place the apple-filled skillet over medium-low heat while you prepare the batter.
In the bowl of a stand mixer (or in a regular bowl with a wooden spoon if you're sans mixer/butch), beat the remaining stick of butter with the brown sugar until light and fluffy, 3 - 4 minutes on medium, scraping down the bowl as necessary. Add the eggs one at a time, beating to combine after each. The batter may break, but that's ok. Whisk or sift together the flours, baking powder, salt and cinnamon into a medium bowl. Stir the vanilla into the crème fraîche. Add half of the flour mixture to the batter, mixing on low until just combined. Add the crème fraîche mixture, stir, then the remaining flour mixture, mixing until just combined. Fold in the chopped apple.
When the apples in the skillet are very tender and the butter mixture has begun to color slightly, after about 20 minutes, remove from the heat and dollop the batter over the apples. Carefully spread the batter with an offset spatula. Place in the oven and bake for 25 - 30 minutes, until the cake is golden and pulling away from the sides of the pan.
Let the cake cool for 5 minutes, then run a knife around the sides of the pan to loosen, and invert a large plate over the pan. Using oven mitts, flip the whole thing over and remove the pan. Some apples/cake may stick to the bottom of the pan; this is easily repaired using a knife or offset spatula to spackle it back together.
Serve the cake warm or at room temperature. It is best the day of baking, but will keep well, tightly covered at room temperature, for a day or two, or refrigerated for up to three days.
Notes
Adapted from The Pioneer Woman.Nutritional values are based on one of eight servings.