Caramelise 30 g sugar and 1 tbsp water in a pot until golden brown. Heat the milk and add to the caramel with the butter. Bring to the boil, add chestnuts, cover and simmer over medium heat for 6-8 minutes.
Stir from time to time. Puree the chestnuts with the stock, let it cool down.
Place the egg yolks, 75 g sugar and vanillin sugar in a metal bowl, whisk over a warm water bath with the whisks of the hand mixer until thick and creamy. Remove from the bain-marie and beat the lukewarm chestnut puree into the egg mixture by the spoonful.
Cut the cream in half. Stir under one half of espresso and cocoa powder. Chill both creams for about 15 minutes.
Whip the cream until stiff. Fold about 100 g cream into the espresso cream and about 150 g cream into the chestnut cream. Layer the creams alternately by the spoonful in 6 cups (each approx. 180 ml)), pull through with a fork (marble).
Cover cups with foil, let them freeze overnight.
Drain the cherries and collect the juice. Bring juice and 25 g sugar to the boil. Mix starch and rum, stir into the boiling juice and simmer again for about 1 minute. Fold in the cherries. Place cups briefly in warm water and turn the ice out onto plates.
Add some of the hot rum cherries. Add the rest of the cherries.