Muddle the halved fig and elderflower liquor together in a cocktail shaker. Add the vodka and lots of ice. With the lid securely on, shake vigorously for at least 20 seconds. Strain through a fine mesh sieve into a low ball glass. Add a few cubes of ice and top with some sparkling wine.
Garnish with a few pieces of the quartered fig and a sprig of thyme. Enjoy immediately.
Figs can vary in size. If the figs you are using are big, then only use one fig. Muddle half of it for the cocktail and garnish with the other half (cut in two).