In the top of a double boiler, heat chopped chocolate and butter over simmering water, stirring occasionally, until melted and combined. Remove from heat, and let cool while you prepare remaining ingredients.
In a medium bowl, beat egg yolks with a hand mixer at medium speed until starting to thicken, about 1 minute. With mixer on medium speed, add ½ cup (100 grams) sugar in a slow, steady stream; increase mixer speed to medium-high, and beat until thick and ribbonlike, 2 to 3 minutes.
Clean mixer attachments. In another medium bowl, beat egg whites with a hand mixer at medium speed until starting to foam, about 1 minute. With mixer on medium speed, add remaining ½ cup (100 grams) sugar in a slow, steady stream; increase mixer speed to high, and beat until stiff peaks form, 7 to 8 minutes.
In another medium bowl, beat cream and vanilla with a hand mixer at high speed until stiff peaks form, 2 to 3 minutes.
Fold egg yolk mixture into cooled chocolate mixture until completely combined. Fold in egg white mixture until combined. Fold in whipped cream. Pour mousse into desired serving dish. Cover and refrigerate until set before serving, at least 4 hours, or up to overnight.
Just before serving, garnish with cocoa and shaved chocolate, if desired. Cover and refrigerate for up to 3 days.