Step 1 In a medium bowl, mix together the chestnut puree, butter, vanilla extract and 2 tablespoons water with a hand mixer until smooth. Set aside.
Step 2 Set a saucepan of water over medium heat and bring to a simmer. Place the egg white in a deep metal bowl that fits over the saucepan without touching the water. Before setting the bowl over the simmering water, beat the egg white with a hand mixer on medium speed just until foamy, about 1 minute. Set the bowl over the simmering water, continuing to beat with the hand mixer (you don't want to let the egg white cook); reduce the heat to medium-low. Slowly add the sugar and beat on high speed until stiff, glossy peaks form, about 6 minutes.
Step 3Immediately fold the meringue into the chestnut puree mixture. Chill for an hour, and up to 3 hours.
Step 4Spoon the mousse into a pastry tube fitted with a large star tip. Pipe the mousse into glasses or bowls. Garnish with shaved chocolate or whipped cream.