Add the blueberries, lime wedges and fresh mint leaves to the glass (or pitcher). Muddle with a wooden spoon so the blueberries are broken and the mint and lime release their juices and flavour. If assembling pitchers you can cover them at this stage and leave in the refrigerator until ready to serve.
Ginger Simple Syrup
1/4 cup grated fresh ginger
1 cup granulated sugar
1 cup cold water
Peel and grate the ginger and add it, together with the sugar and cold water, to a saucepan. Bring it to the boil and stir until the sugar dissolves. Cover and let steep for 15 minutes. Strain and cool in the refrigerator when done.