Heat oven to 375°F.
Pulse chestnuts in food processor until finely ground. Remove to bowl. Stir in vanilla and syrup.
Beat egg whites and salt in medium-size bowl until soft peaks form. Fold into chestnut mixture.
Place phyllo shell in each cup (1-7/8-inch diameter) of mini-muffin tin, for total of 30. Spoon heaping 1-1/2 teaspoons chestnut mixture in each phyllo shell.
Bake in 375°F oven 10 minutes, until golden. Cool on rack. Pipe star of whipped topping on each tartlet.
