One 8-inch springform pan at least 2 1/2 inches high, buttered and bottom lined with buttered parchment or wax paper. Wrap the outside of the pan wrapped with a double layer of heavy-duly foil to prevent seepage. One 10-inch cake pan or roasting pan to serve as a water bath.
Preheat the oven to 425 degrees F.
In large metal bowl set over a pan of hot, not simmering, water (the bottom of the bowl should not touch the water) combine the chocolate and butter and let stand, stirring occasionally, until smooth and melted. Add vanilla.
In a large bowl set over a pan of simmering water heat the eggs, stirring constantly to prevent curdling, until just warm to the touch. Remove from the heat and beat, using the whisk beater, until triple in volume and soft peaks form when the beater is raised, about 5 minutes. Slowly add in sugar while beating.
Using a large wire whisk or rubber spatula, fold 1/2 the eggs into the chocolate mixture until almost incorporated. Fold in the remaining eggs until just blended and no streaks remain. Finish by using a rubber spatula to ensure that the heavier mixture at the bottom is incorporated. Scrape into the prepared pan and smooth with the spatula. Set the pan in the larger pan and surround it with 1 inch very hot water. Bake 5 minutes. Cover loosely with a piece of buttered foil and bake 10 minutes. The cake will appear very soft, which is fine.
Remove from the oven and cool on a rack 45 minutes. Cover with plastic wrap and refrigerate until very firm, about 3 hours.
Unmold: You will need a flat plate at least 8 inches in diameter, covered with plastic wrap as well as a serving plate. Wipe the sides of the pan with a hot, damp towel.
Run a thin metal spatula around the sides of the cake and release the sides of the springform pan. Place the plastic-wrapped plate on top and invert. Wipe the bottom of the pan with a hot, damp towel. Remove the bottom of the pan and the parchment. Invert onto the serving plate.
You can make this tart a few days ahead and refrigerate it until serving. Do not freeze the tart as freezing changes the texture.
Serve at room temperature. Cut into thin slices with a thin sharp knife that has been dipped in hot water. If you use raspberry coulis, either add a spoonful to each plate and set the tart slice on top, or pass the coulis in a small pitcher.
Melt chocolate and butter in a bowl set over a pan of hot water, stirring until smooth. Add milk, corn syrup and vanilla. When cool but not cold, pour over tart, spreading with a spatula or allow it to drizzle down the sides of the tart.