Add the blueberries and simple syrup to a sturdy glass. Gently muddle until the berries release their juices and form a vibrant base.
Tear the mint leaves once or twice to release oils, then add them to the glass. Lightly press with the muddler a few times. Don’t grind the mint—over-muddling makes it bitter.
Squeeze in the juice of half a lime.
Toss in a couple of lime wedges for extra zing.
Add the rum and a small pinch of salt if using. Stir to combine.
Fill the glass with crushed ice. Top with club soda and give it a gentle stir to lift the blueberry-mint mixture from the bottom.
Garnish with a mint sprig and a few whole blueberries.
Serve with a straw so you can sip through the fruit.