Grease a springform pan (26 cm Ø). For the dough, whisk 175 g butter, brown sugar, 1 packet of vanilla sugar and 1 pinch of salt until creamy. Stir in the egg. Mix 150 g flour, ground hazelnuts and oat flakes.
Stir into the butter mixture. Pour the dough into the mould and press a flat base with floured fingers, forming a rim about 4 cm high (the dough is quite soft). Chill for about 1 hour.
Wash the gooseberries, dab dry and clean. Heat jam in a wide pot. Add gooseberries and simmer for about 4 minutes - the gooseberries should not burst open if possible. Remove from the heat and let it cool down.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Spread gooseberries on the floor. Bake in the hot oven for 40-45 minutes on the bottom shelf. Remove and allow to cool.
Coarsely chop the hazelnuts. Roast in a pan without fat. Sprinkle with white sugar and caramelize while turning. Spread on baking paper and let cool off.
Whip the cream until stiff, while pouring in 1 sachet of vanilla sugar. Spread some cream on the cake, sprinkle with nuts. Dust the edge with icing sugar. Add the rest of the cream.