This delectable tart makes an elegant statement without a lot of effort. Luscious ripe mangos sit decoratively atop puff pastry — the shape is up to you, and you can even make this dessert in individual sizes if you like.
This tart doesn’t keep well because the puff pastry gets soggy, so plan on serving it the day you make it.
Cut 3 of the mangos lengthwise into two halves each, slicing as close to the pit as possible. You need 1 cup of peeled, diced mango for the purée; keep the other mango halves intact. Reserve the fourth mango in case it’s needed.
Place the mango cubes in a blender or small food processor and purée until smooth. Transfer the purée to a small saucepan and add the sugar, lime zest and juice, and star anise. Simmer over low heat, stirring frequently, until the purée is reduced by about half, thick and jam-like, 15 to 20 minutes. Transfer to a bowl and chill completely. The purée can be made several days ahead of time and refrigerated until you need it.
Peel the mango halves. Place one half cut (flat) side down and slice into 1/4-inch thick slices, keeping them intact (so that the mango still appears unsliced). If the mangos are very large, cut crosswise slices. Using a wide spatula, transfer the mango to a tray (still intact). Repeat with the remaining mango halves.
Position a rack in the middle of the oven and preheat the oven to 450 degrees F. Butter a rimmed baking sheet or line with parchment paper. Place the buttered baking sheet atop another baking sheet, if possible, to prevent the bottom from burning. Set aside.
Place the puff pastry on the prepared baking sheet. Spread some of the chilled mango purée over the pastry, leaving a 1/2-inch border uncovered around the edge of the dough. Using a wide spatula, transfer one of the mango halves to the pastry, and gently splay the slices with your fingers to arrange them decoratively. Repeat with the remaining mango halves.
Bake the tart for 10 minutes, then reduce the heat to 425 degrees. Sprinkle the top of the mango slices with 2 tablespoons of sugar and continue baking until the puff pastry is golden brown and you can see the mango juices begin to bubble, 15 to 20 minutes more.
Remove the tart from the oven and let cool 5 to 10 minutes before slicing. Serve warm, garnished with a scoop of vanilla ice cream, if you like.