Mango Tarte Tatin

On a lightly floured piece of parchment paper, roll Rough Puff Pastry into a 12×11-inch rectangle (about ¼ inch thick). Cut a 9-inch circle in dough, reserving excess for another use. Evenly dock surface of dough circle. Cut 3 (3-inch) slits in center of circle. Transfer dough circle on parchment to a baking sheet; refrigerate.

Sprinkle sugar evenly in bottom of a 9-inch cast-iron skillet. Cook over medium-high heat, without stirring, until sugar begins to melt. Using a rubber spatula, gently stir sugar around sides of skillet. Cook, stirring occasionally, until sugar turns a deep amber color, about4 minutes, watching carefully. Remove skillet from heat; stir in butter, vanilla, lemon juice, and salt until well combined. Let cool for 15 to 20 minutes.

Preheat oven to 375°F (190°C).

Arrange mango slices in bottom of skillet to completely cover caramel, overlapping as needed. Place cold dough circle on mango, pressing edges of dough inside skillet to fully cover mango.

Bake until pastry is puffed and golden brown, about 30 minutes. Let cool in skillet on a wire rack for 5 minutes. Carefully invert tart onto a serving plate; serve warm or at room temperature.

Freeze cold butter until firm, 15 to 20 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, beat cold butter, flour, and salt at low speed just until butter is coated with flour. With mixer on low speed, add ⅓ cup (80 grams) ice water in a slow, steady stream, beating just until dough comes together, about 1 minute, stopping to scrape sides of bowl and paddle and turn dough to help hydrate evenly. (There will still be large pieces of butter. It is OK if a few dry bits remain.)

Turn out dough onto a lightly floured surface, and roll into a 9-inch square. Wrap in plastic wrap, and refrigerate for 45 minutes to 1 hour.

On a lightly floured surface, roll dough into an 18×10-inch rectangle, lightly flouring surface and top of dough as needed. Fold dough in thirds like a letter. Rotate dough 90 degrees; roll into an 18×10-inch rectangle, and fold in thirds like a letter. Repeat procedure for a third and final turn. Wrap dough in plastic wrap, and refrigerate for at least 1 hour. (If at any point butter is too soft after a fold, wrap dough in plastic wrap, and freeze until butter firms up, checking every 5 minutes).