Wash mint leaves, pat dry and put them in a small mixing bowl. Cover with 3 ounces of Bulleit Bourbon and let soak for 15 minutes.
Remove mint, then place them in a clean cotton cloth and wring over bowl, bruising the leaves. Dip back into bourbon and wring again. Repeat several times to create mint extract. Set extract aside for 1 hour. You can also put the leaves back in the extract for a more concentrated mint flavor.
Combine mint extract (leaves included, if preferred) with simple syrup (1 cup sugar and 1 cup water) in a covered glass container or jar and refrigerate overnight.
Fill julep cups (10-12 oz., preferably silver but glass will do) with crushed ice or shaved ice and insert a fresh mint sprig. Add 1.5 oz. of Bulleit Bourbon to each cup. Add marinated julep mixture to taste.