Set the rack to the lower third of the oven and preheat to 350°F  Dissolve the espresso powder in the water and add the vanilla extract.  Butter an 8 x 3-inch cake pan. Line bottom and sides with parchment paper, extending paper 2-inches above the pan to create a collar.  Set aside.

Place the chocolate pieces and butter in a large heatproof bowl and set over a pan of barely simmering water without allowing the bowl of chocolate to touch the water.  Stir occasionally until melted.  Stir in the espresso/vanilla mixture and set aside to cool.

While the chocolate is cooling, place the eggs into the bowl of a stand mixer and stir in the sugar.  Set the bowl in the same pan of simmering water and whisk until the eggs are warm to the touch and sugar has melted.

Remove the bowl from the water and set on the stand mixer.  Using the whisk attachment beat on medium-high for 8 minutes.  The eggs will quadruple if not more in volume.

Bring the simmering water to a boil for use in the hot water bath, i.e. a bain marie (pronounced “bane mah-REE”).  This is a shallow oven-proof pan just large enough to hold the cake pan.   When ready to bake the gâteau, fill the pan half-full of boiling water.

In 3 separate but equal portions fold the egg mixture into the chocolate mixture.  Pour the batter into the prepared cake pan and set in the bain marie.  Bake for about 40 minutes or until an instant-read thermometer reads 140°F.  Remove the cake pan from the water bath and cool on a wire rack. When cool, refrigerate overnight.

Prior to serving heat the bottom of the cake pan over a low flame. Using an 8-inch cardboard round, place on top of the cake and flip out the cake from the pan.

Flip back over and set on a cake plate. Dust cake with confectioners’ sugar or cocoa powder and serve.   As an alternative, whip the cream and sweeten with confectioner’s sugar.