Fill a large bowl with ice and water, and set aside.
Place 3 tablespoons water in a small bowl. Sprinkle gelatin over water, and let soften for 10 minutes.
Place heavy cream and 1/2 cup sugar in a medium saucepan over medium heat. Bring to a simmer. Add gelatin mixture, and stir until gelatin and sugar are completely dissolved, 1 to 2 minutes. Transfer to 1-quart measuring cup.
Place measuring cup in the ice bath, and whisk cream mixture until cool, 6 to 7 minutes. Add vanilla extract. Pour mixture into six 6-ounce ramekins or glasses. Chill until set, about 1 hour and 50 minutes.
While contents of the ramekins set, make the caramel: Spread remaining cup sugar evenly in the bottom of a heavy skillet, and place over medium-high heat. Let sugar melt without stirring, until the bottom layer is completely melted and the edges begin to brown, 2 to 3 minutes. Tilt and swirl the pan to distribute the sugar evenly. Stir with a wooden spoon until all sugar is melted and dark amber. Stir in 1/2 cup warm water and bourbon. Stir until combined, and remove from heat to cool to room temperature.
To unmold panna cotta, dip ramekins in warm water. Run a paring knife around edges of panna cotta to break seal, and invert each ramekin onto a dessert plate. Dessert will slowly slide out. Garnish with figs and caramel. Serve. You can keep panna cotta, covered in plastic wrap, in the refrigerator for up to three days. It should be eaten quite cold; remove it from the refrigerator just before serving. At times of the year when figs are out of season, drizzle the custard with chocolate sauce, or top it with fresh berries.