Add all the ingredients to a small saucepan, and bring to a boil over medium-high heat. Reduce heat to medium-low. Cook, stirring frequently, for about 5-7 minutes or until figs break down. Let the mixture sit while it cools (about 30 minutes), then strain using a fine mesh strainer.
Add fig vodka, simple syrup and lemon juice to a cocktail shaker filled with ice. Shake vigorously and then pour into ice filled cocktail glasses. Top with soda water. Garnish with sliced figs and thyme sprigs and serve immediately.
This recipe will make enough simple syrup for 10-12 cocktails. Store any leftover fig syrup in a tightly sealed container in the refrigerator for up to one week.