In a martini shaker add whole mint, 8-10 blueberries, blueberry simple syrup, lime juice, rum and ice. Shake well until mint is has released it's flavour, and blueberries are softened.
Pour into a tall glass and add a little club soda. Keep pouring in as much club soda as you enjoy (taste test as you go). About 1/2 cup is good. Top with a few fresh blueberries and lime wedge.