In a heatproof bowl set over a saucepan of simmering water, combine the chopped chocolate, vanilla extract, and unsalted butter. Stir until smooth and fully melted, then remove the bowl from the heat and let it cool slightly.
Separate the eggs while they are cold. Lightly whisk the egg yolks in a small bowl. Once the chocolate mixture has cooled to a warm temperature, gently stir in the egg yolks.
In a clean bowl, beat the egg whites with 3 tablespoons of granulated sugar until stiff peaks form. Be sure to use a clean, dry bowl and whisk for best results.
In another bowl, whip the chilled heavy cream and remaining granulated sugar until soft peaks form.
Gently fold the beaten egg whites into the chocolate and yolk mixture. Use a rubber spatula and fold slowly to keep the mixture light and airy.
Next, carefully fold in the whipped heavy cream until no white streaks remain. Do not over-mix to preserve the mousse’s airy texture.
Spoon the mousse into serving dishes. Cover and refrigerate for at least 4 hours, or overnight for best results. Garnish with extra whipped cream and chocolate shavings if desired before serving.