First, prepare the lemongrass simple syrup by combining sugar, water, and chopped lemongrass in a small saucepan. Bring to a boil, then reduce heat and simmer for 10 minutes. Remove from heat, let cool, and strain to remove lemongrass pieces.

In a cocktail shaker, muddle the blueberries and mint leaves.

Add white rum, lemongrass simple syrup, and lime juice to the shaker. Fill with ice and shake well.

Fill a glass with ice and strain the cocktail mixture into the glass. Top with club soda.

Garnish with additional blueberries and mint leaves, if desired.