Cut the half-a-lime into 5 wedges. Muddle 2 chopped mint, sugar, and 5 pitted cherries at the bottom of a heavy glass. Peel four of the lime wedges, add them to the glass, and muddle again. Fill the glass with ice. Pour in rum and stir gently, then top with a splash of club soda. Squeeze in the juice from the remaining lime wedge and drop into the glass.