Preheat the oven to 250F. Trace 3 circles onto parchment paper, one 7-inch, one 6-inch and one 5-inch. Place the parchment paper face-down onto baking trays.
For the meringue layers, whip the egg whites on low speed and slowly add in the sugar, gradually increasing the speed to high and whipping until they hold a stiff peak when the beaters are lifted. Scrape the meringue into a piping bag fitted with a large plain tip and pipe a spiral of meringue to fill each of the traced circles. Bake the meringues for about 90 minutes, until dry (crack the oven door if the meringues begin to colour at all) and let them cool on the parchment paper.
For the chestnut cream, beat the chestnut puree and 1/2 cup of the icing sugar to smooth. Switch to a whisk and fold in the mascarpone, half of the whipped cream and the vanilla until smooth.
To assemble, place the 7-inch meringue disc onto a platter. Pipe or spread a thick layer of the chestnut cream on it and top it with the 6-inch meringue. Pipe a layer of chestnut cream and top it with the 5-inch meringue. Pipe on the remaining chestnut cream. To finish the torte, fold in the remaining 2 Tbsp of icing sugar into the remaining whipped cream. Spread this on top of the torte and chill until ready to serve.