Lora Brody gave the cake this name (black mouth) because it describes what happens when you eat it. A chocolate lover's dream, this very rich, dense, nearly flourless cake is finished with a really luscious white chocolate cream.
Heat the cream in a saucepan until small bubbles form around the edge. Meanwhile, put the white chocolate in a food processor or in a blender container. Pour the cream over the chocolate; process until completely smooth. Add the Bourbon; taste and add up to a tablespoon more if you like.
Pour into a container with a tight-fitting lid; refrigerate 8 hours. (The cream can be kept in the refrigerator for a week or frozen for up to a month; thaw overnight in refrigerator.).
Heat oven to 350 degrees.
Lightly butter a 9-inch round cake pan; line the bottom with buttered parchment or wax paper. Put the cake pan in a shallow roasting pan; set aside.
For the cake, heat the sugar and Bourbon to a full boil in a small saucepan over medium-high heat. Cook to a syrup, about 2 minutes.
Place the chocolate in a food processor; pour the syrup into the work bowl. Process until the mixture is completely blended, about 12 seconds.
Add the butter, in pieces, with the machine running.
Add the eggs, one at a time.
Add the flour. Process until smooth, about 15 seconds.
Transfer the batter into the prepared pan.
Pour enough hot water into the roasting pan to come about 1 inch up the sides of the cake pan.
Bake until the top is dry, about 30 minutes. Remove the cake pan from its water bath; wipe the cake pan dry.
Cover the top of the cake with a sheet of plastic wrap. Invert the cake onto a flat plate, peel off the parchment.
Quickly but gently invert again onto a serving platter; remove the plastic. Serve the cake warm or at room temperature with the chilled white chocolate cream.