1. Bring sugar and 1 cup water to a boil in a medium saucepan. Boil, stirring often, 1 minute or until sugar is dissolved. Remove from heat; add basil, and cool completely (about 1 hour). Pour into a glass jar. Cover and chill 24 hours. Remove and discard basil.
Mint Simple Syrup: Prepare recipe as directed, substituting fresh mint sprigs for basil sprigs.