Beat the egg whites of large eggs until stiff, add a little salt and cream of tartar with the sugar gradually while beating, add vanilla. Place 6 heaps of snow on a greased baking tray and form shells. Bake at 235 °C for 45 min. Note from me: At this high heat, 45 min might be too much. Once cooled, remove from baking sheet, seal airtight until ready to use.
Filling: mix the chestnut puree well with the sugar, cognac and syrup. Stir in the stiff whipped cream. Place 1 candied kumquat on each filling.
Kumquats can be served very well with this in a cocktail containing lemon juice or vermouth.