Place 8 of the mint leaves in a Tom Collins glass; with a muddler or a wooden spoon, crush the mint leaves until fragrant; set aside. In a cocktail shaker, combine Blueberry Compote, lime juice, simple syrup, remaining mint leaves and rum. Add ice, cover and shake to mix. To the Collins glass, add club soda. Fill glass with fresh blueberries and ice; strain shaker mixture into glass. Garnish with mint.