Score the chestnuts crosswise with a sharp knife on the pointed side and bake in the preheated oven for about 20 minutes at 250 ° until the shell bursts. Rinse with cold water and peel.
Slit the vanilla pod lengthways and cook it together with the chestnuts in the milk for about 45 minutes. The milk is almost completely absorbed by the chestnuts. Fish the vanilla pod out of the pot, finely puree the chestnuts with a hand blender.
Add the rum, cocoa and powdered sugar and stir everything into a smooth cream. Distribute these in 4 dessert bowls. Whip the cream until stiff and serve with the chestnut cream.