Place mint leaves and syrup in a chilled julep cup, and muddle. Pack cup tightly with crushed ice; add bourbon and mint sprig.
1. Mint Syrup: Boil 1 1/2 cups sugar and 1 1/2 cups water, stirring often, 2 to 3 minutes or until sugar dissolves. Remove from heat; add 15 fresh mint sprigs, and cool completely. Cover and chill 24 hours. Strain syrup; discard solids.
2. Grapefruit-Honey Syrup: Prepare Mint Syrup as directed, reducing sugar to 1/2 cup and stirring 3/4 cup fresh grapefruit juice, 1/2 cup honey, 3 (2- x 4-inch) grapefruit rind strips, and rind from 1 lime, cut into strips, into sugar mixture with mint. For julep, muddle with 1 small grapefruit rind strip.
3. Peach-Basil Syrup: Prepare Mint Syrup as directed, substituting basil for mint and stirring 2 (5.5-oz.) cans peach nectar and 1 split vanilla bean into sugar mixture with basil. For julep, muddle with 1 peach slice.
4. Blackberry Syrup: Prepare Mint Syrup as directed, adding 6 oz. fresh blackberries, halved, with mint. For julep, muddle with 2 fresh blackberries.
5. Pineapple-Lemongrass Syrup: Prepare Mint Syrup as directed, reducing granulated sugar to 1 cup, adding 1/2 cup light brown sugar to granulated sugar and water, and stirring 1 cup pineapple juice, 2 Tbsp. fresh lime juice, and 3 (3-inch) pieces fresh lemongrass into sugar mixture with mint after removing from heat. For julep, muddle with 1 small fresh pineapple chunk.