Makes: 8 servings at 56¢ each. Prep Time: 20 minutes. Cook: about 15 minutes. Franois Payard Freeze: 6 hours or overnight. Stand: 45 minutes.
Place the grated chocolate in medium-size bowl.
Combine the milk and all but 1 tablespoon of the sugar in a small heavy saucepan. Place the saucepan over medium heat, stirring constantly, until the sugar is dissolved; continue cooking until tiny bubbles form around the edge of the saucepan.
Whisk together the egg yolk and remaining 1 tablespoon sugar in a small bowl. Pour half of the hot milk over the yolk mixture, whisking quickly. Pour milk-yolk mixture into milk mixture in saucepan and cook, whisking constantly, until mixture thickens slightly and reaches 183°F on instant-read thermometer.
Immediately pour the hot milk mixture over the grated chocolate in the bowl, whisking constantly 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.
Line the bottom of a 6-inch round cake pan or springform pan with aluminum foil, cut to neatly fit. Scrape mixture into pan, smoothing top. Cover with plastic wrap. Freeze 6 hours or overnight.
If using a regular cake pan, immerse the pan in a bowl of hot water for a few seconds. Wipe the bottom and sides of the pan dry; gently loosen the edge of the cake with a thin metal spatula. Invert the cake onto a serving platter. If using a springform pan, cover the outside of the springform pan with thin cloths dipped in hot water and squeezed of excess water. Repeat with the hot cloths until the cake seems loose. Using a thin metal spatula, gently loosen the edge of the cake from the side of the pan; remove the side of the pan. Let the cake stand at room temperature for 45 minutes before serving.
To garnish, run a hot thin metal spatula across the top of the cake to create a wave pattern. Lightly dust the top of the cake with sifted cocoa powder. Serve with whipped cream, if desired. Wrap any leftover cake in plastic wrap and refrigerate. Let the leftovers stand at room temperature for 10 minutes before serving.