Line the bottom of a 9-inch springform pan with parchment paper. Butter bottom and sides. Set the pan on a sheet of aluminum foil cut 2 inches larger than the pan, and wrap the edges of the foil up around the sides of the pan. (The pan will be sitting in water, and this will help prevent leaks.)
Melt chocolate and butter over low heat, stirring until smooth. Set aside to cool.
Blend the following into the eggs, one ingredient at a time: sugar, then cocoa, then vanilla. Slowly add the chocolate, while mixing. Pour into the springform pan.
Now create the bain-marie (waterbath). Place cakepan into a larger pan, and pour in an about an inch of very hot water around the springform pan. Bake 45 minutes in a preheated 325 degree oven, until the edges are set. (If you do the 'toothpick test', do it an inch from the edge of the cake. The center will still be moist.)
Remove the sides of the pan and allow the cake to cool on the springform base. Don't worry if the center sinks a bit - it's supposed to. When the cake has cooled completely, invert and remove the base and parchment. Dust with cocoa power and decorate with chocolate shavings, or place a dollop of whipped cream in the center and top with mint leaves.