In a small saucepan, combine sugar, water, and fresh thyme. Heat over medium heat until it reaches a gentle simmer—about 5 minutes. Remove from heat, cool, and strain out the thyme.

Juice 1 lemon until you have about 1 ounce of fresh lemon juice. Strain through a fine mesh sieve.

In a shaker or large jar, combine fig jam, botanical gin, lemon juice, and cooled thyme syrup. Stir or shake until smooth.

Fill glasses with ice and strain the cocktail mixture over the ice.

Garnish with a sprig of thyme or slice of fig.