Preheat the oven to 350 degrees F.
Grease a 9 1/2 by 13 1/2 by 3/4-inch pan. Cut waxed paper width of pan plus 5 inches in length. Line the pan so there is at least 2 inches of waxed paper extending over both ends of the pan. Grease the paper.
Separate the eggs, and beat the yolks with the sugar, until they are light, creamy and thickened.
Using clean beaters, beat the egg whites until stiff. Stir the chocolate into the yolks and fold in the beaten egg whites. Gently combine. To facilitate this, put a small amount of whites into the yolk and chocolate mixture and then add all this back into the whites.
Spread the chocolate mixture evenly in the prepared pan and bake for 10 to 15 minutes. Shut off the oven and bake 5 minutes more. Practice will tell you if the timing is right.
Remove from the oven and cover top with a dishtowel wrung out in cold water. Stretch the cloth tight and tuck under the pan. Cool, and refrigerate 1 hour.
Remove the cloth carefully and loosen edges with knife. Dust top heavily and completely with cocoa. Lay 2 pieces of waxed paper longer than the pan side by side overlapping with the top over the bottom. Turn out cake on bottom end of paper and carefully pull off the waxed paper.
Whip the cream over a bowl of ice, and add the sugar and vanilla when it begins to thicken. Beat until stiff.
Spread the cake with the whipped cream, with less towards the top. Roll the cake from bottom, the long side forward, using the waxed paper to roll it. When rolled, the paper should be all around it so you can mold it with your hands as you finish. Put on a long wooden board to chill for a few hours.
When ready to serve, open the paper and cut off along side with the tip of a knife. If there are cracks along the side, dust all over with the cocoa in a shaker or use a small sieve or sifter to distribute it where needed.