Melt the chocolate together with the butter over a low heat.
Stir to homogenize the mixture.
When the mixture is completely smooth, turn off the heat.
Add the vanilla and sugar and stir again. Set the cream aside.
In another bowl, mix the flour, cocoa, a pinch of salt, and the baking powder. Use a spatula and mix gently.
Separate the whites from the yolks. Put the whites in the mixer bowl.
Stir the yolks into the chocolate cream then add the dry ingredients, carefully folding in. Add the milk to thin the mixture.
Beat the egg whites with a pinch of salt until stiff. When you have a nice foam, fold them into the chocolate cream with upward movements.
Preheat the oven to medium heat (180 C degrees or 356 Fahrenheit) and line a 22-24 cm (8.6-9.4 inch) diameter cake tin with baking paper.
Pour the mixture into the pan and level.
Bake the cake for 25 minutes.
Turn off the heat and leave it in the oven for another 5 minutes, then remove and place on a cooling tray to cool.
When it has completely cooled, place it on a plate.