For the cake: Preheat the oven to 350 degrees F. Grease an 8-by-8-inch baking pan.
Using a stand mixer fitted with the paddle attachment, mix the cream, sugar and eggs together. Sift the flour, cocoa powder and baking soda over a piece of wax paper or a large bowl. Add the dry ingredients to the wet ingredients and mix until light and fluffy. Stir in the vanilla extract. Pour the batter into the prepared pan and bake for 30 minutes.
Cool the cake completely in the pan.
For the frosting: In a medium saucepan set over medium heat, bring the cream, sugar and cocoa to a simmer, stirring to dissolve the sugar, about 5 minutes.
Continue to cook until a candy thermometer inserted in the mixture reaches the soft-ball stage or 238 degrees F, about 20 minutes. To test for the soft-ball stage, scoop a teaspoon of the frosting into a bowl of cold water.
When rolled between your fingers, the frosting in the cold water should form a soft ball. Remove the frosting from the heat, and stir in the vanilla.
Working quickly, spread the frosting over the top of the cake. Let the frosting stiffen up on the cake, about 20 minutes.
Cut the cake into 2-by-2-inch squares, and then serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.