For the dough: Put flour on the work surface. Create a well in the center and add egg yolk to well. Cut butter into small pieces and distribute around the flour. Add a pinch of salt and combine everything with a pastry cutter. Shape into a ball, wrap in foil and chill for 30 minutes.
Grease a springform pan with butter. Roll out dough on a floured surface, press into the pan, taking care to go up the edges. Prick with a fork several times.
For the filling: Drain gooseberries or rinse fresh gooseberries. Spread gooseberries evenly over dough.
Combine cream cheese, sugar, vanilla sugar, eggs, lemon zest, pudding powder and cream fraiche. Mix until creamy and pour over gooseberries.
Bake in preheated oven at 180°C (approximately 350°F) for about 45 minutes. Remove and let cool.
Heat gooseberry jam, strain through a sieve and brush onto cake. Release cake from pan and let cool. Dust with powdered sugar and serve.