Preheat the oven to 180 degrees C. Grease the cake tin or springform pan by putting a big piece of foil smoothly across the base and then the ring over the top. Leave about 2cm extra foil out of the spring form pan and fold up so no caramel can escape from the pan.
Apple Topping: Peel apples and remove the core. Half of the apples thinly cut into slices slices (about 1/2cm). The other half into thicker 1cm slices.
Melt the butter in a large frying pan then saute the thick apple slices for 4-6 minutes at medium temperature, turn it a few times. The apples should not be falling apart and quite soft.
Add the thin apple slices, lemon juice and brown sugar and continue to cook for 1-2 minutes until the sugar dissolves. Here again from time to time contact, so that the sugar is evenly distributed. Place the apple mixture evenly on the bottom of the prepared spring form pan.
Tart Batter: Melt the butter then leave to cool slightly. Sift together the flour with cornflour, baking powder and salt.
In a mixer bowl add the sugar, brown sugar and cooled butter. Beat for 1 minute with the electric mixer then add the eggs, sour cream and vanilla. Place the flour mixture into the butter mixture and mix on high until well blended.
To Assemble: Put the batter on the apples and smooth. Bake in the preheated oven on the bottom shelf for 40 minutes or a toothpick comes out clean.
Let cool for 20 minutes in the spring form pan. Carefully run a plastic knife along the edge and carefully remove the tart. Allow to cool completely before serving.