Mix yeast with sugar and lukewarm milk. Cover, and leave to rest for 20 minutes at 35° C.
Melt the butter, then add the eggs, vanilla sugar, salt and rum. Sieve in the flour combine. Add the milk-yeast mixture and mix well. Then beat the dough until it forms bubbles. Leave to rise fo 20 minutes.
Roll out the dough to a 1-inch thickness, cut out rounds, fill them with jam and close well. Place the buns with the closed side down next to each other in a buttered tin and brush each one generously with melted butter.
Cover with a tea towel and leave in a warm spot for 15 minutes.
Bake in the oven pre-heated to 180°C for around 30 minutes.
Take out of the oven and leave to cool slightly, then turn out and serve warm (with custard if you like).