Syrup: Remove the lemon rind, skipping as much white pith as possible, with a vegetable peeler. Add to a food processor with the ginger and chop finely. Transfer to a saucepan with the sugar and water and bring to a boil. Simmer for 15 minutes, strain and cool.

Fill a cocktail shaker with ice, add the vodka, ginger syrup, and lime juice, then shake like crazy for 30 seconds. Strain into a chilled cocktail glass, and garnish with the lime twist.