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1
Preheat oven to 200°C; arrange oven rack in middle position.
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2
Heat 80 g butter and sugar in 28 cm cast-iron or steel tarte Tatin mold or heavy ovenproof skillet over medium-high heat, stirring with wooden spoon until golden caramel forms (5 minutes).
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3
Remove from heat; add vanilla seeds and extract; arrange apple halves cut-side up in concentric circles, fitting them snugly; sprinkle with salt.
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4
Cook over medium-high heat for 8 minutes, basting apples with caramel; remove from heat.
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5
Lay puff pastry sheet over apples, tucking edges down inside mold; prick with fork.
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6
Bake 25–30 minutes until pastry is golden brown and apples are very tender when pierced with knife.
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7
Remove from oven; let cool 5 minutes, then invert onto serving plate in one smooth motion, allowing caramel to drip over pastry.
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8
Serve warm or at room temperature with crème fraîche or vanilla ice cream.