Preheat oven to 180°C/350°F. Use 1 tbs of your butter to rub all over the inside of a 22cm/9in springform pan, then line the base and sides of the pan with baking or parchment paper (the paper will stick to the butter and stay put).
Place the remaining butter and the chocolate into a large heatproof bowl. Set the bowl over a saucepan with a couple of inches of water in the bottom (make sure the water doesn’t touch the bottom of the bowl), and place the pan over medium heat so the water comes just to simmering point. Melt the butter and chocolate, stirring every now and then, until it’s completely smooth, then remove from heat and allow to cool for a few minutes so the mixture is lukewarm.
Using a whisk, mix the egg yolks into the cooled chocolate and butter. Add the sieved cocoa powder and salt and whisk well to combine, then whisk in the vanilla.
Put the egg whites into the bowl of a stand mixer fitted with the whisk attachment (you can do this step by hand with a large whisk, but you’ll have to get your arm muscles ready!). Whisk on medium-high speed just until the whites form very soft peaks when you lift the whisk.
Reduce your mixer speed to medium and slowly begin adding the sugar to the egg whites. Continue whisking and adding the sugar a couple of tablespoons at a time, until the sugar is used up and the mixture forms glossy, stiff peaks when you lift the whisk. If you rub a little of this mixture between your fingers it should feel smooth, with no grittiness from the sugar at all.
Using a metal spoon or a spatula, stir about a quarter of the egg white mixture into the chocolate mixture until combined. Then, working gently, scoop the rest of the egg white mix into the chocolate bowl and fold together until everything is just mixed and there are no streaks of egg white. The aim is to keep as much air in the batter as possible, so don’t overmix.
Gently pour the batter into the lined pan and smooth the top. Bake until the cake is set and barely risen, with a thin crust on top, about 35 minutes. It will not test clean with a skewer, but should be set enough that it doesn’t jiggle when you move the pan.
Cool the cake completely in the pan before removing and serving in thin slices with extra melted chocolate and thick cream or ice cream.