Adjust an oven rack to the lower-middle position, place a baking stone on the rack, and heat the oven to 500 degrees. Let the baking stone heat for at least 30 minutes (but no longer than 1 hour).

Heat 2 tablespoons of oil in a medium nonstick skillet over medium-low heat until shimmering. Stir in the onions, brown sugar, and salt. Cover and cook stirring occasionally, until the onions are softened and have released their juices, about 10 minutes. Remove the lid, increase the heat to medium-high, and continue to cook, stirring often, until the onions are deeply browned, 10 to 15 minutes.

Turn the dough out onto a lightly floured counter, divide it into 2 equal pieces, and cover with greased plastic wrap. Working with one piece of dough at a time (keep the other piece covered), press and roll the dough into a 14 by 8-inch oval on a lightly floured counter. Transfer the dough on a piece of parchment paper and reshape as needed. Gently dimple the surface of the dough with your fingertips.

Brush the dough liberally with additional oil and season with pepper. Scatter half of the caramelized onions, figs, turkey, walnuts, and blue cheese evenly over the tart, leaving a 1/2-inch border around the edge. Slide the parchment paper and tart onto a rimless (or invertebaking sheet, and then slide the tart (still on the parchmenonto the hot baking stone (or the overturned, preheated rimmed baking sheet).

Bake until the tart is deep golden brown 8-10 minutes, rotating it halfway through baking. (Prepare the second tart while the first bakes). Remove the tart from the oven by sliding the parchment paper back onto the baking sheet. Discard the parchment paper, slide the tart onto a cutting board, and sprinkle with half of the scallions. Let the stone (or overturned rimmed baking sheereheat for 5 minutes before baking the second tart. Serve warm.