Melt the white chocolate in a double boiler. Whisk in 8 ounces of the heavy cream until well blended. Remove from the heat. Let the mixture sit for 20 to 30 minutes to come to room temperature.
Combine 2 cups of the cream and 3 tablespoons sugar in a large, chilled mixing bowl. Use a hand mixer or standing mixer to whip the cream and sugar until stiff peaks form when the beater is stopped and lifted out.
Gently fold a third of the melted white chocolate mixture into the whipped cream. Add the second third; fold in, then add the remainder.
If your mousse becomes soft, it’s no cause for alarm. Chill in a bowl for 15 to 20 minutes, and it will be as good as new.
Serve in a big bowl, family-style, and top the mousse with the grated dark chocolate.
For a more elegant presentation, fill a pastry bag equipped with a star tip and pipe the mousse into individual glasses or bowls. Sprinkle with grated white or dark chocolate, and top with sweet whipped cream.