Cut the zest (colored portion of the peel) off the clementines, taking care to scrape away and discard all of the bitter white pith clinging to the zest. Add the zest to a large clean container or jar large enough to hold the peels and vodka. Reserve fruit for another use.
Pour the vodka over the zest and seal the container. Let sit undisturbed in a cool, dark place for 3 to 4 weeks.
Place 2 cups sugar and 2 cups water in a saucepan and heat until sugar is dissolved; remove from the heat. Let the sugar syrup cool to room temperature.
Add half of the cooled syrup to the orange peel-vodka mixture, stir and taste. If it’s not sweet enough, continue adding more syrup until it's to your taste.
Pour the clemencello through a funnel lined with a coffee filter or cheesecloth into small containers or one container large enough to hold the liquid and seal.
Store clemencello in the freezer; it shouldn't freeze. To serve, pour into small glasses and offer it for dessert with a plate of biscotti and/or chocolate truffles or use as you would limoncello.