Special equipment: a small wooden skewer and a small strainer
Add the blueberries to a cocktail shaker and crush with a muddler. Add the gin, Fresh Mint Syrup and enough ice to fill the cocktail shaker. Cover tightly and shake vigorously for a few seconds, until the mixture is very cold. Double-strain into a lowball glass filled with crushed ice. Top with a splash of club soda. Thread 3 blueberries and the mint sprig on a small skewer and set on the side of the glass for garnish. Serve immediately.
Stir together the sugar and 3/4 cup water in a small saucepan. Bring to a simmer over medium heat and cook until the sugar completely dissolves, 3 to 5 minutes. Turn off the heat. Use your hands to tear the bunch of mint in half and add it to the saucepan. Using a spoon, press down the mint to make sure that it is completely submerged. Allow the syrup to cool to room temperature in the saucepan, about 1 hour. Strain the mixture through a fine-mesh strainer set over a small bowl or liquid measuring cup. Use the back of a spoon to press down on the mint to extract as much flavor as possible. The syrup can be used immediately and will keep in the refrigerator for up to 2 weeks.