With the rack in the middle position, preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the puff pastry into two 10-inch (25 cm) squares. Place one square on the prepared baking sheet and refrigerate the other.
Brush the surface of the dough with 1 tbsp (15 ml) of the butter and sprinkle with 1 tbsp of the sugar. Cover with a piece of parchment paper and a second baking sheet.
Bake for 35 minutes or until golden brown. Remove the top baking sheet. Let the puff pastry cool on its baking sheet, on a wire rack. Once both baking sheets are completely cooled, repeat the steps with the remaining puff pastry.
Meanwhile, in a small bowl, sprinkle the gelatin over 2 tbsp (30 ml) of the milk. Let bloom for 5 minutes.
In a saucepan off the heat, combine the sugar and cornstarch. Whisk in the egg yolks. Stir in the remaining milk and the cream. Bring to a boil over medium heat, whisking constantly, scraping the sides and bottom of the pan, until the mixture has thickened. Remove from the heat and strain the pastry cream.
In a microwave, melt the gelatin mixture until it has dissolved.
Stir the gelatin mixture and butter into the pastry cream. Cover with plastic wrap directly on the surface of the cream. Let cool and refrigerate for 2 hours or until completely chilled. When ready to use, stir with a spatula or whisk to soften.
With a serrated breadknife, trim the puff pastry to obtain two 9-inch (23 cm) squares.
In a bowl, whip the cream and sugar using an electric mixer until semi-firm peaks form. Spoon the whipped cream into a pastry bag fitted with a 1/2-inch (1 cm) plain tip. Set aside in the refrigerator.
Place 1 piece of puff pastry onto a large serving platter. Spread with half of the pastry cream, then half of the mango butter. Layer with the second puff pastry, the remaining pastry cream and mango butter. Decorate the surface of the pastry by piping 25 large whipped-cream teardrops 1 1/2 inches (4 cm) in diameter. Refrigerate for 1 hour before serving.