Melt the chocolate and butter in a heatproof bowl set over a pan of barely simmering water (don’t let the bowl touch the water). Stir occasionally until completely smooth, then remove from heat and let cool slightly.
Whisk the egg yolks with 2 tablespoons of sugar in a separate bowl until pale and thickened. This should take about 2-3 minutes of vigorous whisking.
Slowly pour the melted chocolate mixture into the egg yolk mixture, whisking constantly to prevent the eggs from scrambling. The mixture should be completely smooth and glossy.
Beat the egg whites with a pinch of salt in a clean, grease-free bowl until soft peaks form. Gradually add the remaining 2 tablespoons of sugar and continue beating until stiff, glossy peaks form.
Whip the cold heavy cream with vanilla in another bowl until it holds soft peaks. Be careful not to overwhip or it will become grainy.
Gently fold one-third of the whipped egg whites into the chocolate mixture to lighten it. Use a rubber spatula and a gentle cutting and folding motion to preserve the air in the whites.
Fold in the remaining egg whites until just barely incorporated—a few streaks are preferable to overmixing and deflating your mousse.
Fold in the whipped cream using the same gentle technique until the mixture is uniform but still light and airy.
Divide the mousse into individual serving glasses or bowls, cover with plastic wrap, and refrigerate for at least 4 hours or preferably overnight.
Before serving, garnish with chocolate shavings, a light dusting of cocoa powder, or a dollop of whipped cream if desired.