Place the chocolate in a medium bowl and set aside. Combine the milk and all but 1-tablespoon of the sugar in a small saucepan. Heat over medium heat, stirring constantly until the sugar is completely dissolved. Stop stirring and cook until the milk begins to bubble around the edge of the pan. Remove the pan from the heat. Whisk together the egg yolk and the remaining 1-tablespoon sugar in a small bowl. Pour half of the hot milk over the yolk mixture, whisking constantly to combine. Return the mixture to the saucepan and cook, whisking constantly, until the mixture thickens slightly and reaches 185 degrees F on an instant-read thermometer. Immediately pour the mixture over the chocolate. Whisk until the chocolate is melted. Add the butter 1/2-tablespoon at a time, whisking until the butter is melted and the mixture is smooth. Whisk in the vanilla. Scrape the batter into a 6-inch round cake pan and smooth the top with a rubber spatula. Cover the pan with plastic wrap and place it in the freezer for at least 6 hours, or overnight. To unmold the cake, carefully immerse the pan in hot water for a few seconds. Wipe the bottom and sides of the pan dry and invert the cake onto a serving platter. Decorate the top of the cake by running a hot dull knife across its surface in a wave pattern (dip the knife in hot water and wipe completely dry before using it). Lightly dust the top of the cake with sifted cocoa powder. Allow the cake to stand at room temperature for 45 minutes before serving. Store leftovers in the refrigerator. Note: It is important that the butter be at room temperature, or it will not blend completely into the chocolate mixture and there will be a small lumps of butter in the cake. You can make this 2 or even 3 days in advance and freeze it. When you need it, unmold it and let it stand at room temperature for 45 minutes so its not freezer cold. Or unmold it and then store in the freezer, whole or cut into portions, for up to 2 months.
Recipe courtesy of Francois Payard