Make the fig simple syrup: simmer the fig preserves, water and vanilla over medium-low heat in a small saucepan. Stir until the mixture loosens and becomes syrupy.
Strain into a separate container. Use a wooden spoon to press down on the strainer to release as much syrup as possible.
Fill a cocktail shaker with ice. Pour the vodka, lemon juice and fig syrup into the shaker. Shake vigorously for 10-15 seconds. Pour into a martini glass.