Add lemon quarters, mint leaves, and sugar to a large cocktail glass. Use a muddler to firmly press down and twist, releasing the lemon juice from the lemon pieces.
Pour in rum and fill the glass with ice. Stir to combine.
Top with soda water. Garnish and serve.
Notes
Big Batch Option: To serve 8, you will need 8 lemons (seeds removed and quartered), 2 1/2 cups mint leaves, 1/3 cup granulated sugar, 2 cups white rum, 4 cups soda water. Muddle together lemon quarters, mint leaves, and sugar together in the bottom of a pitcher. Add rum and fill with ice. Stir to combine. Top with soda water and serve.