Place the sugar and the water in a small saucepan over medium heat. Bring to a boil, stir, and then remove from the heat. Let cool completely (put it in the refrigerator to speed this along). This is the simple syrup.

Remove the mint from the stems. Slice three of the limes into eight sections each.

Place the mint and the lime sections into a large pitcher. Use a pestle, wooden spoon, or meat mallet to crush the mint leaves and the limes. Make sure to crush each of the lime sections until they release their juice.

Add the blueberries and crush those, too. It doesn’t have to be perfect—some of the blueberries can still be whole.

Pour in the rum and the simple syrup from step 1. Stir to combine. Refrigerate until ready to serve.

When ready to serve, stir the club soda into the pitcher. Cut the remaining lime into eight wedges.

Place ice in each individual glass and pour the blueberry mojito mixture over the top.

Garnish with a lime wedge and more mint. Serve immediately.