For the apricot cake, first line a baking sheet with parchment paper and preheat the oven to 190 °C. Mix flour, baking powder, vanilla sugar and lemon zest. Cream butter and sugar.
Beat in eggs one at a time and add 2 tablespoons flour per egg. Finally, stir in the rum. Spread the dough on the prepared baking sheet and cover with halved apricots.
Bake in the preheated oven at 190 °C for about 30 minutes. Sprinkle the cooled apricot cake with powdered sugar and serve.