Put the cherries, 2 tablespoons sugar and the rum in a medium saucepan and cook over medium-high heat until syrupy, about 15-20 minutes. Remove from the heat and let cool, then refrigerate until very cold, 2-3 hours.
In the meantime, heat the milk and the remaining ½ cup sugar in a saucepan over medium-low heat, whisking so the sugar dissolves.
Whisk the egg yolks in a small bowl.
Gradually whisk about ½ cup of the warm milk mixture into the eggs, then whisk the egg mixture into the saucepan. Cook and stir constantly, until the mixture coats the back of a spoon and registers 168 degrees F on a candy thermometer, about 15 minutes.
Remove from heat; add the semisweet and unsweetened chocolate and the butter and set aside until the chocolate melts, about 5 minutes.
Transfer the chocolate mixture to a blender and puree until smooth. Pour into a large bowl and stir in the heavy cream and vanilla. Refrigerate until chilled, 2-3 hours or overnight.
Strain the cherry mixture while reserving the syrup. When the ice cream is very thick, add the cherries and continue churning until incorporated. Transfer to a freezer-safe container.
Drizzle in the reserved cherry syrup and swirl with a spoon. Cover and freeze until firm, at least 4 hours.
Recipe by Wishes and Dishes at https://wishesndishes.com/chocolate-cherry-ice-cream/