Drain the cherries while collecting the juice. Boil up the juice, wine, sugar, aniseed, cinnamon and lemon peel. Simmer covered for 5-10 minutes
Stir starch and 2 tablespoons of water until smooth. Stir into the hot juice and simmer briefly. Remove the pot from the stove. Stir in rum and cherries and let it cool down a bit
Remove the cinnamon stick, star anise and lemon peel if necessary and divide the punch cherries into 4 glasses. Place 1 scoop of ice cream on each and decorate