Preheat oven at 400 F
Cut each fig in 4 from tip to tail.
In a pan, heat sugar, butter, and 2 tbsp of water without stirring until you get a light caramel color.
Add the vinegar, stir to smooth texture.
Grease well your 9-inch pie dish or mold. Pour the caramel into the mold, cover the bottom, and let cool 2 minutes.
Arrange the quarters of figs on top of the caramel, placing them somewhat tight, side by side, in one layer, making two concentric circles. I added a couple of quarter figs on the top of one layer to cover holes.
Put the disc of dough, on the whole, edge by sliding the turn of the dough in the empty space, to the bottom of the mold. Poke the dough all over with a fork.
Bake 25-30 min until the crust is lightly golden.
Transfer to a wire rack and let it rest for 10 minutes.
Take off the dough lightly with a knife if needed.
Place a flat serving dish on top of the pie dish, flip upside down quickly in one shot to unmold the pie and let the tart fall gently out of the pan before removing the pie dish or mold.
Serve lukewarm or at room temperature.