Combine first 3 ingredients in a chilled julep cup; mull gently until sugar dissolves.
Add enough finely crushed ice to fill cup three-fourths full. Add bourbon, and stir gently. Add additional crushed ice to fill cup. Freeze for at least 15 minutes. Before serving, garnish with a fresh mint sprig.
Note: Mint Juleps should be made individually and preferably in a julep cup.