Combine the sugar and the egg whites and heat to 50°C (122°F).
Whisk continuously in a mixer until completely cool then add the vinegar. Pipe 13 cm long meringues using a 1.5 cm basketweave nozzle. Once cooked, these meringues will be positioned on the sides of the dessert. Pipe the base using a 0.8 cm nozzle.
Bake at 95°C (203°F) for 2 h.
Blend the chestnut paste and cream with the rum. Push through a drum sieve then pipe as for truffles (35 g) using a 12 mm diameter plain nozzle and freeze.
Whip the ingredients together using a mixer.
Pipe 35 g of Sublime cream with vanilla onto a sheet of plastic wrap. Insert the chestnut filling in the middle (35 g). Seal the plastic wrap making the cream come up to form the Mont Blanc. Freeze. Position a meringue in a 6 cm ring mould and pipe in 10 g of chestnut filling then cover with Sublime cream and remove the mould. Add a piece of meringue, then finish with the Mont Blanc and a few candied chestnut trimmings.