How to Make It
Combine 1 cup water and sugar in a small saucepan. Bring to a boil; cook 1 minute. Remove from heat. Stir in ginger, 2 Thai basil stems (reserving leaves), and kaffir lime leaves. Cover sugar mixture; let stand 10 minutes. Strain over a bowl; discard solids.
Place 1/2 cup crushed ice in each of 6 glasses. Add reserved basil leaves to each glass; stir gently to bruise leaves. Add 2 tablespoons sugar mixture, 1/2 cup prosecco, and 1 lime wedge to each glass. Stir gently; serve immediately. Reserve remaining sugar mixture for another use.