Melt the chocolate by adding to a bowl placed over simmering water and stirring until melted and smooth. Remove from the heat.
Whisk together the egg yolks, 4 tablespoons sugar, 3/4 cup heavy cream and a pinch of salt in a medium 2-quart curved bottom saucepan. Place over medium heat and stir constantly until the mixture is thick, about 3 minutes. Whisk in the chocolate and vanilla. Strain the mixture into a large bowl using a fine mesh sieve and place in the refrigerator until chilled, at least 30 minutes.
Beat the remaining 1 cup heavy cream and remaining 2 tablespoons of sugar until stiff peaks form. Gently fold the whipped cream into the chilled chocolate. Divide the mousse evenly among 4 individual serving dishes and cover with plastic wrap. Place in the refrigerator to chill for at least one hour. Serve with shaved chocolate.