Place the Twang-a-Rita Nectarberry on a small plate. Run the lime wedge around the rim of a high-ball glass and dip into rimmer, twisting to coat evenly.
In a cocktail shaker, combine strawberries, mint, and simple syrup. Muddle together until the leaves start to break down. Add rum and lime juice. Top with ice.
Shake until well combined and pour into prepared glass. Finish with club soda and garnish with strawberry and mint sprig.