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Preheat the oven to 350°. Line a baking sheet with parchment paper. On a lightly floured surface, roll the pastry out to a scant 1/4-inch thickness. Cut out four 4-inch rounds. Place the rounds on the sheet; freeze for 5 minutes.
Using a fork, prick the dough all over. Cover the rounds with parchment and another baking sheet. Bake for about 20 minutes, until the pastry is golden and crisp. Remove the baking sheet and the top layer of parchment. Scatter the cheese over the pastry and arrange the figs on top. Bake for 5 minutes, until the cheese is melted and the figs are warm.