Separate the egg yolks from the whites. In a deep bowl, beat the butter with a mixer. Gradually add 1/2 cup sugar to it and then the yolks.
Once the sugar is dissolved, start adding the flour and chocolate (pre-melted in a water bath) to the mixture. Whip the egg whites to foam with the remaining 1/5 cup sugar and add them to the other products. Brush the bottom of a baking dish with a little butter, sprinkle it with a pinch or two of flour, dusting off the excess.