1 cup granulated sugar
1 cup water
1 4-inch piece of fresh ginger, peeled and grated on the large holes of a box grater
2 cups tightly packed fresh mint leaves
1 bottle white rum
1 1/2 cups freshly squeezed lime juice
12 fresh mint leaves
In a small saucepan, bring the sugar, water, and ginger to a boil over high heat, stirring to dissolve the sugar, about 5 minutes. Remove from the heat and add the first amount of mint leaves, stir to combine, and let cool at room temperature, about 1 hour. Place a fine mesh strainer over a 1 1/2-2 qt container and strain the syrup, discarding the solids. Add the rum and lime juice and stir to combine. Cover and refrigerate until well chilled. Fill glasses with ice. Add 1/2 cup mixture and top with 2 tbsp club soda. Stir to combine. Garnish with mint sprig.