Whisk egg yolks and sugar in a medium heatproof bowl until thick and pale.Advertisement
Bring 2 cups cream to a boil in a medium saucepan. Gradually pour into yolk mixture, whisking constantly to combine. Pour back into pan; cook, stirring constantly, over medium heat until thickened and mixture registers 185 degrees on an instant-read thermometer, about 10 minutes. Remove from heat. Whisk in gelatin.
Put chocolate into a heatproof bowl. Pour hot custard through a fine sieve over the chocolate. Let stand 2 minutes. Whisk until shiny and smooth. Let cool.
Put remaining 5 3/4 cups cream into the bowl of an electric mixer fitted with the whisk attachment; beat on medium-low speed until soft peaks form (do not let it get stiff). Gently fold into chocolate mixture in 3 batches. Cover, and refrigerate overnight before using.