Place the vodka, ginger mint syrup and lime juice in a cocktail shaker filled with ice. Shake and strain into a glass filled with ice cubes. Top with club soda, garnish with mint leaves and the lime wedge before serving.
Ginger Mint Syrup:
Place the sugar, water, ginger, mint and a pinch of salt into a small saucepan and cook over low heat, stirring until the sugar is dissolved. Remove from the heat and let steep for 20 to 30 minutes and strain once cooled. Alternatively, place the saucepan in a medium bowl filled with ice water and strain once cooled. Makes 6 to 8 servings.