Melt chocolate in top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching. Let cool slightly, about 10 minutes.
Pour aquafaba into the bowl of a stand mixer fitted with a whisk attachment. Beat on high speed until fluffy and quadrupled in volume, about 1 minute. Add xanthan gum and beat for 30 seconds. Add confectioners’ sugar and vanilla sugar; continue beating until foam is firm and glossy, about 2 minutes more.
Fold melted chocolate gently into whipped foam until thoroughly incorporated. Transfer to a lidded container.