Preheat the oven to 200°C (approximately 400°F). Carve chestnuts with a sharp knife, place on a lined baking sheet and roast for 15-20 minutes until shells pop.
Remove, let cool slightly and peel while still warm. Reserve 6 pieces for the garnish. Put peeled chestnuts in a pot. Pour in milk sliced vanilla pod. Allow to simmer for about 30 minutes until soft.
Remove vanilla pod and discard. Remove chestnuts and press through a potato ricer. Combine powdered sugar, cocoa and rum. Whisk in some of the vanilla milk and add the chestnut puree.
Beat cream until stiff. Pour puree into bowls and garnish with whipped cream and chestnuts. Serve immediately.