In a small saucepan, heat cherries over medium heat. Cook until soft, using the back of a spoon to mash cherries. Add confectioners’ sugar and rum; cook until slightly thickened, to 8 minutes. Strain through a fine-mesh sieve, discarding cherry pulp. Refrigerate for minutes.

In a large saucepan, bring milk to a simmer over medium heat, whisking occasionally. Whisk in chocolate until smooth. Whisk in all but 2 tablespoons cherry sauce. Garnish with whipped cream and remaining 2 tablespoons cherry sauce, if desired.