Simmer the sugar and water until dissolved; remove from the heat, add the mint, cover, and steep 15 minutes.
Strain the syrup, discard the leaves, and chill until cold.
Chill 4 julep cups or rocks glasses in the freezer.
Gently muddle 8 to 10 mint leaves in each cup — press, do not shred.
Add 1 ounce mint syrup and 2 ounces bourbon to each cup.
Fill each cup with crushed ice, mounded above the rim.
Stir until the cup frosts, then top with more ice.
Garnish with a slapped mint sprig, add a short straw, and serve immediately.