1. Fill a martini shaker with 1 cup ice. Add lime wedges, lime juice, and mint. Muddle lime and mint with a pestle or a long spoon until well-bruised and fragrant.
2. Combine honey, rum, and club soda; stir gently to dissolve honey. Add to muddled mixture; stir until mixture is well-chilled. Strain into a rocks glass filled with ice; garnish with mint and lime, if desired.