Start by filling a tall glass with ice and set it aside.
In a cocktail shaker, mix together fresh lime juice, sweet syrup, and fragrant Thai basil leaves. Use a muddler to gently press the basil for about 10 seconds to release its oils.
Add rum and a cup of ice to the shaker. Secure the lid and shake the mixture vigorously until the outside of the shaker becomes frosty, about 10 to 15 seconds.
Carefully strain the mixture into the prepared glass and top it off with club soda. Stir gently to combine.
For a finishing touch, garnish your drink with a lime wedge and a sprig of Thai basil, if you like.
