Boil 50ml water and sugar in a saucepan until the thermometer reaches 121°C.
Whisk egg whites in a clean bowl until stiff peaks form.
Pour hot sugar syrup into whites in a thin stream while whisking slowly until glossy.
Continue whisking at slow speed for 5 minutes until almost completely cooled.
Melt chocolate with 30ml water in a pan, then whisk in half the cream and boil.
Remove from heat, whisk until smooth, then incorporate the remaining cream.
Place sponge on a plate, drizzle with Armagnac, and center the ice cream on top.
Spread half of the meringue over the base and pipe the remainder on top.
Caramelise the meringue using a blow torch or a very hot oven for a few seconds.
Serve the dessert immediately with the warm chocolate sauce.