For the bottom: First of all, whisk sugar with room temperature butter to combine. Add sour cream, egg and mix well. Then add flour mixed with baking powder and salt. With your hands (or combine) knead the batter. Batter should be elastic, soft and non sticky
Filling:Cut apples in small pieces, pour sugar, add butter (room temperature), stir well and cook on low heat. When boiling, cook for another 10 minutes.
Sauce:Beat eggs with sugar to combine, add sour cream, rum extract, mix very well. Pour flour and mix again. Batter should be thick like sour cream.
Crumbs: Grate cold butter, add sugar, baking powder and mix with your hands.
When done these first steps, spread your baking tray with butter, pour with some flour. Then add pie bottom mixture all allow the tray bottom, do a little board. Then pour chilled apple filling. Then add the sauce, pour everything with crumbs. Put in the 180C (360F) preheated oven and bake about 40 minutes. Then cover the top with some foil and bake for another 20-30 minutes. Try it with some ice cream.