Preheat the oven to 350°F (180°C) and butter six (6-ounce) oven-safe mugs or ramekins. Place on a deep baking sheet and set aside.
Melt the chocolate and butter together either over a double boiler or gently in the microwave. Set aside to cool.
In the bowl of a stand mixer fitted with a whisk attachment (or with a medium bowl and handheld electric mixer) whip the egg whites on high speed until soft peaks are formed, about 4 minutes.
Gradually add ⅓ cup (2½ oz/71g) of sugar, one tablespoon at a time, and then continue to whip to stiff, glossy peaks, about 2 more minutes.
Transfer the whites to a clean bowl, then add the yolks and remaining sugar to the stand mixer and whip on high speed until pale and thickened, about 5 minutes.
To the yolks, add the cooled chocolate mixer until combined. Then remove the bowl from the machine.
Using a metal spoon, fold ⅓ of the whites into the chocolate mixture to loosen it. Once incorporated, fold in the remaining whites.
Divide the mixture evenly among the prepared mugs or ramekins, then top with a piece of bittersweet chocolate.
Bake for 15-20 minutes, until puffed and slightly cracked.
While baking, whip the cream to soft peaks in a medium bowl with a handheld electric mixer or by hand with a wire whisk. Refrigerate until ready to use.
Let the baked hot chocolate rest for 5 minutes, then top with a generous dollop of whipped cream and serve immediately. If there are leftovers you can reheat in the microwave for 45 seconds or so.