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1
Pulse together flour, confectioners sugar, and salt in a food processor until combined. Add butter and process until mixture resembles fine meal. Add 3 yolks (reserving the fourth for egg wash) and process until it forms a smooth dough, 2 to 3 minutes. (Don't worry about overworking dough.) Transfer dough to a work surface and gather into a ball, then divide into 3 equal pieces. Form one third of dough into a small disk, then form remaining dough into a larger disk. Chill disks, each wrapped in plastic wrap, until firm, at least 1 hour.
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2
Simmer figs, water, sugar, and cinnamon in a 1- to 2-quart heavy saucepan, uncovered, stirring occasionally, until mixture is thickened, 2 to 3 minutes. Stir in sesame seeds (3 tablespoons) and cook, stirring, 1 minute. Remove from heat and stir in orange-flower water, then transfer filling to a bowl. Cool filling to room temperature, about 30 minutes.
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3
Put oven rack in middle position and preheat oven to 350u00b0F. Line a baking sheet with parchment paper and place flan ring in center.
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4
Roll out larger disk of dough into an 11-inch round on a lightly floured surface with a floured rolling pin. (If dough is too firm to roll out, let stand at room temperature 5 minutes.) Fit dough into flan ring, pressing dough up side of ring (dough is very tender and tears easily; patch as needed; they will blend in during baking), then trim dough flush with top of ring. Spoon filling into crust and spread evenly.
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5
Roll out remaining disk of dough into a 9-inch round on lightly floured surface with floured rolling pin. Gently lay round over filling, then roll rolling pin over top to trim. Patch if necessary.
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6
Beat together remaining yolk and cream (1 tablespoon) in a cup with a fork and brush some of egg wash over top crust, then chill until egg wash appears darker and is slightly tacky, about 3 minutes. Brush with second coat of egg wash and chill again. Lightly score top with back of a small knife to make a decorative pattern and sprinkle with sesame seeds (1 teaspoon).
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7
Bake tart until top is golden, 30 to 35 minutes. Transfer tart on baking sheet to a rack and cool 10 minutes, then slide tart off parchment onto rack to cool. Gently remove ring.
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8
While tart bakes, stir together cream, honey, zest, and cardamom in a medium bowl and chill, covered. Just before serving, beat cream mixture with an electric mixer until it holds soft peaks.
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9
Serve tart, warm or at room temperature, with cream and oranges.
