Divide and layer cut lime wedges, mint leaves, and blueberries between two highball/collins glasses.
Add the simple syrup (or granulated sugar) and use a metal or wooded muddle to gently crush the contents of the glass together for about 30 seconds. This allows the oils and juices to release and blend, creating the signature drink flavor.
Pour the lime juice and rum into the glasses, then fill them almost to the top with crushed ice. Add a splash of sparkling water, seltzer, or club soda and stir well.
Garnish with a lime wheel or wedge, whole blueberries, and sprigs of mint, if desired.