Step 1

Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper and set aside.

Step 2

Carefully unfold the puff pastry on a lightly floured surface and roll out to a 10 1/2-by-10 1/2-inch sheet. Use a sharp knife to cut out a 10-inch circle. Transfer the disk to the prepared baking sheet and refrigerate while preparing the filling.

Step 3

Whisk the cornstarch, lemon juice and vanilla extract together in a small bowl until smooth; set aside.

Step 4

Sprinkle the sugar over the bottom of an 8-inch ovenproof skillet and cook over medium-low heat, stirring frequently, until the sugar is melted and amber brown, about 5 minutes. Remove the skillet from the heat and whisk in the cornstarch mixture and cubed butter until smooth, 35 to 40 seconds. (The cornstarch and butter will cause the caramel to bubble rapidly and may appear curdled, but it will smooth out after about 30 seconds of continuous whisking; stick with it and it will become silky-smooth.) Whisk in the salt, cardamom and cinnamon.

Step 5

Carefully arrange the figs cut-side down on the caramel in tight concentric circles, making sure there is as little space as possible between the figs. (The raw figs may look crowded but will shrink considerably during baking; gently nudge them into place with fingers or a fork as space between the figs will cause the pastry to sag when the tart is flipped out of the skillet.)

Step 6

Place the pastry round on top of the figs and use a fork to tuck the edges down around the figs. Poke the pastry all over with a fork. Bake until the pastry is golden brown and the caramel is bubbling around the edges, 35 to 40 minutes.

Step 7

Let the tart cool for 5 minutes in the skillet; any longer and the caramel will harden as it cools, making it difficult for the tart to release from the skillet. Place a serving plate or cake stand on top of the skillet. Using oven mitts, carefully flip the skillet over to invert the tart onto the plate. Lift off the skillet; replace any figs that become dislodged. Let the tart cool for at least 30 minutes before slicing and serving with vanilla ice cream or whipped cream.