For the Rumgugelhupf, cream butter (melted) with vanilla sugar and sugar until fluffy. Gradually stir in eggs and milk. Stir in flour and baking powder.
Mix in melted (slightly cooled) chocolate. Pour the dough into a greased and rolled out Gugelhupfform and bake at 180 °C (convection oven) for approx. 50 minutes (needle test).
Turn the hot Gugelhupf out of the mold and immediately pour rum over it.