To a martini shaker add, the vodka, ginger syrup, mint, and lime juice. Shake and serve in a chilled martini glass.
In a small saucepan add the water, ginger and sugar. Stir to combine and bring to a boil. Continue to heat on a simmer to make a simple syrup, about 20 minutes. When ready, strain and transfer to a glass container and allow to cool to room temperature.