1 Preheat oven to 400 degrees. Place puff pastry circles in refrigerator. In a small saucepan, combine brown sugar, rum, and pinch of salt; bring to a boil over medium-high heat. Boil 1 minute, then add butter and stir until completely melted. In a jumbo muffin pan, divide sugar mixture among the cups, about 4 teaspoons each. Divide mango among cups and top with pastry. Bake until pastry is golden brown, puffed, and juices are bubbling, 20 to 25 minutes, rotating pan halfway through.
2 Let cool on a wire rack, 15 minutes. Run a small knife around edges of pastries to loosen. Place a rimmed baking sheet over pan and quickly invert to release tartlets. Serve warm.