Whisk the eggs with the sugar until fluffy. Pour in the oil and milk. Mix the flour, cocoa, baking powder and salt and stir them into the batter. Pour the batter into a 20 cm cake tin lined with baking paper. Bake at 170 °C for about 30 minutes, then let the sponge cool completely.
Whisk Babička butter with the powdered sugar until fluffy. Add Babička quark, Babička sour cream and the vanilla sugar.
For a firmer cream, add the stabiliser. Put the cream in the fridge for 15 minutes to set slightly.
Hollow out the sponge and crumble the removed cake into crumbs. Spread the jam over the base and arrange the bananas, cut in half, on top. Pile the cream on top into a dome. Sprinkle with the cake crumbs and chill for at least 2 hours, ideally overnight.