Cut the limes in half and squeeze them to make 1 cup of fresh lime juice.
Add mint leaves to the pitcher and muddle gently to release the oils.
Pour in the lime juice and simple syrup. Muddle again to mix.
Add the white rum and stir well.
Fill the pitcher halfway with ice cubes.
Top with club soda and stir gently.
Garnish with lime wheels and extra mint sprigs.
Notes
The pitcher can be prepared up to 4 hours ahead without ice and club soda. Store in the fridge.Add ice and club soda just before serving to keep the drink fizzy.For a non-alcoholic version, replace rum with extra club soda.Fresh lime juice makes a big difference - skip bottled juice.The drink stays fresh in the fridge for up to 24 hours but might lose some fizz.