Preheat oven to 180 degrees C. Lightly grease a 23cm springform cake tin.
In a medium bowl, mix together the butter and sugar until smooth. Mix in 1 egg then stir in the baking powder and flour. Knead together into dough. Press into the bottom and up the sides of the prepared tin.
Mix together the cottage cheese, oil, 3/4 cup white sugar, vanilla sugar and pudding mix in a large bowl until smooth. Blend in the egg yolks, egg, milk and lemon juice; pour mixture into the prepared pan.
Bake in preheated oven until the filling no longer moves when you shake the pan, about 1 hour.