Preheat oven to 325°F (165°C). Place six 6-ounce ramekins in a large roasting pan. Boil water in a kettle for the water bath.
Blend fresh mango chunks until completely smooth, then strain through a fine-mesh sieve to remove any fibers. Measure 1 cup of purée and set aside.
In a medium saucepan over medium heat, warm the heavy cream until it just begins to steam and tiny bubbles form around the edges. Remove from heat immediately.
In a large mixing bowl, whisk together egg yolks, 1/3 cup granulated sugar, and salt until pale and slightly thickened, about 1 minute. Add the mango purée and vanilla, whisking until fully combined.
Slowly pour the warm cream into the egg mixture in a thin stream while whisking constantly to temper the eggs. Strain the entire custard mixture through a fine-mesh sieve into a large measuring cup with a spout.
Divide the custard evenly among the six ramekins. Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the ramekins.
Bake for 35-40 minutes, until the custards are set around the edges but still jiggle slightly in the center when gently shaken. Remove ramekins from water bath and cool to room temperature on a wire rack.
Cover each ramekin with plastic wrap and refrigerate for at least 4 hours or overnight until completely chilled and firmly set.
Just before serving, gently blot any moisture from the custard surfaces with a paper towel. Sprinkle 1 tablespoon superfine sugar evenly over each custard.
Using a kitchen torch held 4-5 inches away, move in circular motions to caramelize the sugar until it turns deep amber and forms a glassy shell. Let sit for 1 minute before serving to allow the sugar to harden completely.