Preheat the oven to 350 degrees F and grease and line a 9-inch spring form pan with parchment paper. Set aside. You can also use a 9-inch cake pan.
Peel and slice the apples into 3/8th inch cubes. Place them in a separate bowl and set aside.
1 pound apples, like Granny Smith or Honeycrisp
In a medium bowl, whisk together the flour, baking powder and salt. Set aside as well.
210 grams all-purpose flour,8 grams baking powder,3 grams salt
In a bowl of a stand mixer, cream the butter and sugar on medium speed for about 3-4 minutes, or until light and fluffy. Scrape the bottom and sides to ensure that everything is incorporated.
226 grams unsalted butter,200 grams sugar
While still mixing on medium speed, add one egg yolk at a time. Scrape the bowl to ensure that everything is incorporated as well. The butter mixture should be pale yellow in color.
3 egg yolks
Add the rum, sourdough discard, and vanilla to the egg mixture and mix on low. If the batter looks curdled, this is okay.
60 grams rum *see substitutions below,120 grams sourdough discard,8 grams vanilla extract
Pour the flour mixture into the wet ingredients. Use a rubber spatula to fold the flour into the batter. When there are just a few streaks of flour left, pour in the apple pieces and continue to fold into the batter until all of the flour and apples have been incorporated. The batter will be thick.
Pour the batter into the prepared pan and spread it to be an even layer. Finally sprinkle the remaining sugar on top of the batter.
To long-ferment: Cover the batter and place in the fridge overnight. Just before baking, sprinkle the top of the batter with the sugar. Bake as normal.
40 grams sugar, for topping
Bake for 45-50 minutes or until the internal temperature is 205 degrees F or a toothpick in the center comes out clean.
If you substitute the rum for water, apple juice or milk, beginning checking the cake for doneness around 35 minutes. Continue to check every 5 minutes after until fully baked.
Let the cake come to room temperature. Then just before serving, dust powdered sugar on top. Serve with vanilla ice cream and enjoy!