Muddle the mint gently: Add mint leaves to the empty pitcher. Pour in the simple syrup. Press the leaves with a muddler 6–8 times until fragrant. Do not shred the mint.
Add lime and rum: Pour in fresh lime juice and white rum. Stir to combine so the mint oils blend into the base.
Chill the base: Cover and refrigerate 30–60 minutes to marry flavors. You can chill up to 24 hours.
Add ice and bubbles: Right before serving, fill the pitcher halfway with ice. Top with chilled club soda. Stir gently from the bottom to lift the mint without knocking out the fizz.
Garnish and serve: Add lime wheels and fresh mint sprigs. Pour into ice-filled glasses and top off with a splash more soda if you like extra sparkle.
Too tart? Add 1–2 tablespoons more simple syrup.
Too sweet? Add a squeeze of lime and a splash of club soda.
Too strong? Add more ice and club soda; stir and taste again.
