For the dough mix crème fraîche, sugar, vanilla sugar, oil and 5 tablespoons of milk. Mix flour and baking powder. Knead first with the dough hooks of the mixer, then with your hands to a smooth dough.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Grease the springform pan (26 cm Ø). Roll out the dough to a rectangle (approx. 30 x 38 cm) on a floured work surface.
Spread with red fruit jelly, leaving a margin of about 2 cm all around. Chop the nuts coarsely and sprinkle them on the groats, except for 2 tbsp. Roll up the dough from the long side and cut into 10 pieces. Place upright in the form.
Bake in a hot oven for about 30 minutes.
Remove from the oven and let it cool down. Carefully remove from the mould and leave to cool on a cake rack.
For the icing, stir icing sugar with 4 tablespoons of milk until smooth and drizzle over the cake. Sprinkle with the rest of the hazelnuts.