For the yellow plum cake, put the flour in the mixing bowl of the food processor. Crumble in the yeast and sprinkle with sugar, add a pinch of salt.
Add vanilla sugar, butter and the egg and mix everything with the dough hook to a smooth yeast dough. Cover the dough and let it rise in a warm place until it has doubled in volume (about 1 hour).
In the meantime, wash, halve and pit the plums. Knead the risen yeast dough again with your hands, then roll it out on a floured baking sheet.
Place the plums on the dough with the round side down, sprinkle with cinnamon sugar and bake in the oven at 200° C for 40 minutes, then leave to bake for another 10 minutes in the reheat with the oven turned off.
Allow the cake to cool slightly, then place on a cooling rack to cool definitively.