Cover the baking sheet with parchment paper or grease and flour, preheat the oven to 160 °.
Halve the apricots, remove the stones. Sift the flour with baking powder, beat the eggs, salt, vanilla sugar, lemon zest, cinnamon and 3/4 of the powdered sugar until frothy.
Let the oil run in while stirring constantly.
Mix the flour mixture with the rest of the powdered sugar and fold in carefully. Finally add the rum.
Cover with apricots and bake for about 35 minutes on the lowest rack.