Sin City's Gin Gin Mule

First enjoyed at New York's Bemelman's Bar at The Carlyle, The Gin Gin Mule is another Saunder's creation. My only suggestion for enhancement is to be in the company of beautiful ladies, as I was that evening.

2 ounces gin
3/4 ounce fresh lime juice
1/2 ounce ginger simple syrup*
Ginger beer
6 – 8 mint leaves, plus a sprig for garnish

*2 ounces ginger, thinly sliced
1 cup sugar
1 1/2 cup water
1 1/2 teaspoons whole black peppercorns
Combine the ginger, sugar, water, and peppercorns in a medium saucepan over medium heat. Bring to a simmer, stirring until the sugar dissolves. Continue simmering for 30 to 40 minutes or until the syrup smells very gingery. Remove from heat and cool completely. Strain the syrup through a fine sieve, transfer to a bottle, and refrigerate.