If the mango is extra juicy, place the slices in a colander to drain for 30 minutes.
Adjust the oven rack to the center and preheat the oven to 400°F.
Melt the butter in an 8-inch oven-safe frying pan (with a steel handle). Add the sugar and allow it to melt slowly, without stirring, over medium heat. Tip the pan frequently to help the sugar to melt.
When the sugar is golden, add the mango slices and turn up the heat. The mangoes will release their liquid. Cook the mixture for about 10 to 15 minutes, stirring frequently (but gently to avoid breaking up the mangoes, but making sure they are evenly glazed), until the liquid has thickened to a caramel consistency. Remove from the heat.
Meanwhile, roll out the puff pastry large enough to more than cover the mango (a standard store-bought sheet of puff pastry should be large enough as is, and can simply be trimmed at the corners to make it round). Pack down the mango and then cover with the pastry, pushing down the sides. Cut a small hole in the center of the pastry.
Bake for about 20 to 30 minutes or until the puff pastry is puffed and golden brown. Remove from the oven (caution: the handle will be extremely hot; this is easy to forget once it’s out of the oven. Leave a kitchen towel over the handle to remind yourself until it cools), rest for a couple minutes, and then invert onto a plate and serve with vanilla ice cream, if desired.