Mix butter and sugar with the whisks of the mixer until creamy. Stir in vanilla extract and crème fraiche. Briefly stir in 350 g flour until crumbly, then knead into a smooth dough with your hands.
Roll out the dough on slightly floured cling film to form a rectangle (approx. 23 x 30 cm). Stir the jam until smooth and spread it on the dough, leaving an approx. 4 cm wide edge on one long side.
Roll up the dough from the other long side (which is spread to the edge) using the foil and chill for about 2 hours.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Line two baking trays with baking paper. Cut the roll of dough into slices just under 0.5 cm thick. Place them on the baking tray with a little space between them.
Bake in a hot oven for about 10 minutes one after the other. Remove and let cool on a cake rack.