On a lightly floured piece of parchment paper, roll Rough Puff Pastry into a 12x11-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.