For the apples: Preheat the oven to 350 degrees F. Butter the bottom and sides of a 9-inch springform pan and sprinkle with some maple sugar to coat the butter.
Heat a 12-inch cast-iron skillet over medium heat and add the 2 tablespoons butter. Add the apples and maple sugar and stir to combine. Saute until caramelized, but not cooked through, about 5 minutes. Remove from the heat and set aside.
For the crumble: Mix the cornmeal, flour, oats, light brown sugar, maple sugar, cinnamon and salt in a bowl. Add the diced butter and use a fork to mash the ingredients together until they become coarse crumbs.
For the cake: To the bowl of a stand mixer fitted with a paddle attachment, add the butter, maple sugar and syrup and whip until light and fluffy. Add the eggs and creme fraiche, mixing on low speed. Add the flour, baking soda, allspice, cinnamon, cloves, nutmeg and salt and stir to combine. Stir in the vanilla extract. Add the batter to the prepared springform pan, topping with the sauteed apples. Gently nestle the apples into the cake batter.
Put the crumble topping over the apple mixture. Put the springform pan on a baking sheet and bake until cooked through, about 1 hour. Allow to cool slightly, about 15 minutes, before removing from the pan. Slice into wedges and serve.