Put the 1 g gelatin sheets to soften in cold water. Peel the 3 mangoes, remove the pits. Puree the pulp in a blender. Heat it in a saucepan. Add the drained gelatine sheets. Leave to cool.
Pour the liquid cream into a terrine, beat it into whipped cream, gradually incorporating the powdered sugar and vanilla sugar. Gently add to the mango puree. Pour the rum and 20 cl of water into a deep plate, quickly pass the biscuits through this mixture and place 12 of them vertically, on the edges of a 11-size charlotte mould. Pour the mango mixture into the mould. , pack well and place the 3 remaining biscuits on top. Put in the fridge and let set for at least 3 hours.
When ready to serve, cut the last mango into slices. Put them in a pan with the butter and sugar and brown them for 2 minutes.
Invert the charlotte onto a serving platter, dust it with icing sugar, arrange the mango slices nicely on top and serve.
You can accompany this charlotte with a passion fruit coulis. Optionally add chilled mint or lemon balm leaves.