Set the oven at 325 degrees. Lightly butter a 9-inch layer cake pan, line the bottom with a circle of parchment paper cut to fit in, and butter the paper. Have on hand a roasting pan.
In the top of a double boiler over hot but not boiling water, melt the chocolate and butter, stirring until smooth. Stir in the coffee and vanilla. Remove the top of the double boiler and wipe the bottom.
In a large bowl, whisk the eggs, extra yolks, and sugar. Slowly whisk in the chocolate mixture. Whisk in cocoa powder and salt.
Transfer the batter to the cake pan. Set the cake pan in the roasting pan. Place the roasting pan in the oven. Pour enough warm tap water into the roasting pan to come halfway up the outside of the cake pan.
Bake the cake for 45 minutes, rotating from front to back halfway through baking, or until the cake is set. Do not let it cook until the top is hard or the cake may dry out.
Remove the cake pan from the water bath and leave to cool; refrigerate overnight.