• This recipe is for 10-inch springform pan or 10-inch oven-proof skillet with at least 2 inches of height to prevent overflowing during baking. You can half the recipe and bake in 7-inch springform pan or 7-inch oven-proof skillet or round pan.
• 30 minutes to 1 hour before you start to work on this recipe, take the butter, eggs, and sour cream out of the fridge to let the butter softened and let the eggs and sour cream come to a room temperature
• Preheat the oven to 350 F (180 C) for conventional oven. Please lower the temperature by 20 F (15 C) if using a convection oven
• Butter the bottom and the sides of the pan or skillet. Dust with about 2 Tbsp (or more as needed) of sugar all over. The sugar should stick to the butter. Tap out any excess sugar
  
• If you use a round baking pan, I recommend butter the bottom and then line the with parchment paper for easier removal. You can skip the sugar dusting. Then butter the sides and dust with sugar and tap out excess sugar

Prepare the apple:

• I leave the apple unpeeled. Core all the apples. Finely dice one of the apple.
  
• Thinly slice the rest of the two apples. We will use the sliced apples for the top of the cake
  

Prepare the cake batter:

• Combine all-purpose flour, baking powder, baking soda, and salt
• In a stand mixer fitted with a paddle attachment, combine roasted chestnuts, vanilla extract, and sugar. Beat on low for about 1 minute. This will break down the chestnut into smaller pieces.
  
• Add the softened butter and continue to beat on medium-high until the butter is light and fluffy, this takes about 4-5 minutes. Scrape the side of the bowl
  
• Add egg, one at a time
  
• Beat until combined before adding another one. Beat until light and smooth
  
• Add 1/2 of the flour mixture and then beat on a low speed to combine
  
• Add sour cream and rum and beat until almost combined. Then add the rest of the flour and beat until the batter is smooth and well combined
  
• Use a flexible spatula to scrape the side of the bowl and also fold the mixture several times to make sure everything is well-mixed.
  
• Add the diced apple pieces and gently fold them in
  
• Scrape the batter into the prepared pan/skillet. Smooth the top with spatula.
  
• Use about 5 to 6 apple slices, spread them out like a fan, and place them on top of the batter. Repeat with the rest of the apple slices. It's okay to overlap slightly. You may or you may not have leftover apple slices. If you do, well, it's your snack then :)
  
• Sprinkle 30 grams of sugar evenly on top of the batter and apple slices
  

Bake the cake:

• Place the pan/skillet in the center of the oven and bake for 50-60 minutes or until the edges are golden brown and the cake is springy to the touch. If you insert a cake tester into the center of the cake, it should come out with a bit of sticky crumb is fine, but it shouldn't be wet

Cool down:

• Let the cake cool down completely in the pan, which may take 2-3 hours or longer.
  

Serve:

• I like to serve the cake the day after because I feel like the flavor has developed even more. If you use a springform pan, loosen the side of the cake with an offset spatula and then remove the outer ring. Cut into desired sizes and serve as is or with a bit of whipped cream or cream fraiche