To make Mint Syrup: 1 cup water; 1 cup sugar; 1 cup fresh mint leaves. Bring ingredients to a boil in a saucepan and stir until sugar dissolves, then simmer for 1 minute. Remove from heat and let mixture steep. Strain into a jar and let cool.
To make the cocktail: Mix all ingredients in a cocktail shaker with ice. Pour over ice in a mule mug. Garnish with lime slices and mint leaves.