Peel and segment the clementines. Add to a cocktail shaker along with a couple fine grates of the fresh ginger. Raw ginger is potent so only add a touch unless you really want a strong ginger flavor. Muddle well until all the clementines have been pressed and the juice released. Add lots of ice to the shaker along with the vodka and St. Germain.
With the lid securely on, vigorously shake for 15-20 seconds. Strain into a martini or another kind of cocktail glass. Enjoy while cold!