Preheat the oven to 350F and position the rack in the center of the oven. Grease and lightly flour two 9-inch cake pans or 16 muffin tins.
Make a chocolate and cocoa syrup (see the Note on chocolate and water ):
Chop the chocolate into ½-inch pieces and combine with the cocoa in a medium-sized bowl. Bring 1 cup of water to a boil and gently whisk half of the hot water into the chopped chocolate. (The chocolate will begin to seize a bit.) Whisk in the remaining hot water and continue whisking until you have a shiny, thick, smooth chocolate syrup, 2 minutes. Add the vanilla extract. Set the syrup aside and allow it to come to room temperature.
Cream the butter and incorporate the eggs (see the Note on creaming butter and "Room-temperature eggs" in the Notes section, below):
Place the butter in the bowl of the stand mixer with the paddle attachment and beat on medium speed for 1 minute. Add the sugar and beat on medium-high speed until the mixture becomes fluffy and almost white in color, 6 to 8 minutes, stopping the mixer occasionally to scrape down the sides of the bowl. Add the whole eggs one at a time, and continue to beat until they are fully incorporated. Add the egg yolk and beat until the batter looks smooth and glossy, 30 seconds.
Assemble the dry ingredients.
In a dry bowl, whisk together the dry ingredients.
Combine the flour and the chocolate syrup:
With the mixer on slow speed, add half the dry mixture and beat until the flour is just incorporated. Add all the chocolate syrup and continue mixing on slow speed. Add the second half of the dry ingredients and beat until the batter is thoroughly combined. Scrape down the sides and bottom of the bowl with a rubber spatula and briefly beat the batter on medium speed for 20 seconds.
Bake the cake:
Scrape the batter into the prepared pans, evening out the batter with a rubber spatula. Run a paring knife in a single circular motion through the batter, 1 inch from the edge of the pan. This will help the cake to rise evenly. Bake the cakes until the center is set and a tester inserted in the middle of the cake comes out clean, approximately 25 to 30 minutes. If you are making cupcakes, bake them for 20 to 25 minutes.
Allow the cakes to cool on a wire rack for about 20 minutes. Run a paring knife around the outer sides of the pan and invert the cakes onto cooling racks. Allow the cake layers to cool to room temperature.
Make the frosting:
In the bowl of a bain-marie, melt the chocolate. Remove the bowl from the heat. Heat the cream in a small saucepan. Add the hot cream to the melted chocolate, whisking continuously, to make a shiny, smooth ganache. Place the bowl of ganache in the refrigerator, scraping the bowl with a rubber spatula every 5 minutes, until the ganache is slightly chilled, around 60F.
In the bowl of a stand mixer, or with a hand mixer, whisk the slightly chilled ganache together with the salt, powdered sugar, and the slightly chilled butter on medium speed for 4 to 6 minutes. The icing should hold the lines of a whisk, increase in volume, and become a much lighter shade of brown.
Fill and ice the cake:
If the individual cake layers domed a bit too much, use a long serrated knife to trim the peaked tops to even out the tops. Place the bottom layer on a decorative serving plate. Cut a 12-inch-long piece of wax paper into 4 equal strips. Place each strip under an edge of the cake to cover the rim of the plate, to prevent it from becoming coated with icing (see illustration, page 50). Using an offset spatula, smear a generous layer of icing over the bottom cake layer, making sure to smear an equal amount of icing around the outer edge of the layer. Place the second cake layer on top. Evenly ice the whole cake with the remaining icing. Once you have smoothed out all the rough edges, remove the wax paper strips from underneath the cake to reveal a spotless serving platter beneath your finished cake.
Serving Suggestions:
Serve this cake at room temperature with a glass of milk or a cup of tea. It needs no accompaniment. I also recommend using the Cinnamon Caramel Mousse --Karen Waltucks favorite--and the Sesame Milk Chocolate Mousse as delicious, lighter alternatives to the ganache filling.
