Combine apple slices and cinnamon in a saucepan and cook over low heat for 10 minutes. If necessary, add a tiny bit of water so apples don't burn. Remove from heat and set aside to cool.

Preheat the oven to 350 degrees F (175 degrees C). Grease a 10-inch springform pan with butter.

Combine butter, sugar, vanilla sugar, and egg in a large bowl; beat using an electric mixer until smooth and creamy. Mix flour and baking powder in a separate bowl. Add 2/3 of flour mixture, 1 tablespoon at a time, to butter mixture and beat on low speed. Add remaining flour mixture and mix in by hand to make a crumbly dough.

Transfer 1/2 the dough into the prepared springform pan and press down to create a bottom crust. Add apple slices, leaving a small space around the edges. Crumble remaining dough evenly on top.

Bake in the preheated oven until streusel and crust are lightly browned, about 50 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Carefully transfer to a serving plate or cooling rack.