I'm actually not sure what to call this. Possibilities are "Ugly Chocolate Dessert" (because it's less structurally sound than a normal cake, so it tends to break and look pretty bad) or "Elitist Chocolate Dessert" (because you pretty much have to be a serious chocoholic to like it).
This is a slightly modified version of "Le Gateau Victoire au Chocolat, Mousseline", from Julia Child and Company.
Locate a 13"x9"x2" cake pan, and another pan large enough to hold the cake pan. Fill the larger pan with enough water so that, when the cake pan is in the larger pan, the water comes halfway up the smaller pan. Put the oven rack in the bottom third of the oven, put the larger pan (with water) in the oven, and preheat the oven to 350 degrees. Butter the smaller pan, line the bottom with wax paper, butter the wax paper, then "flour" the pan with unsweetened cocoa (or flour).
Break up the chocolate into a saucepan, and add the espresso. Bring 2" water to a boil in a larger pan. Remove the larger pan from the heat, set the chocolate pan in it; cover the chocolate pan and let the chocolate melt.
Break the eggs into a large bowl, add the sugar, and stir over hot water for several minutes until the eggs are slightly warm. Beat for about 5 minutes, until the mixture has at least tripled in volume and forms a thick ribbon when a bit is lifted and falls from the beater; the eggs should be the consistency of lightly whipped cream. (You must have beating equipment that will keep the whole mass of egg moving at once, meaning a narrow rounded bowl and a beater that circulates around it continually.)
Pour cream into a chilled metal mixing bowl. Beat until cream has doubled in volume and holds its shape softly. Whip in the vanilla.
Beat up the melted chocolate with a whisk; it should be smooth and silky. Scrape it into the egg-sugar mixture, blending rapidly with a rubber spatula, and, when partially incorporated, fold in the whipped cream, deflating cream and eggs as little as possible. Turn batter into prepared cake pan, which will be about 2/3 filled. Set at once in the pan of hot water in the preheated oven. Cake will rise some 1/8" above edge of pan, and is done when a skewer or straw comes out clean -- after about 1 hour of baking. Then turn off oven, leaving oven door ajar, and let cake sit for 30 minutes in its pan of water, so that it will sink evenly. Remove from oven, still in its pan of water, and let sit for another 30 minutes so that it will firm up before unmolding and serving. Cake will sink down as it cools to about its original volume.
This cake is at its most tender and delicious when eaten slightly warm; however, you may cook it even a day or two in advance, leave it in its pan (covered when cool, and refrigerated), then set it in a 200 degree oven for 20 minutes to warm gently.
Unmold the cake and decorate with a sprinkling of confectionsers sugar, or with pipings of whipped cream, or with a soft chocolate icing (semisweet chocolate melted and beaten with a little soft butter). You may wish to pass a custard sauce or sweetened and vanilla-flavored whipped cream with the cake.
Laura