Set up a double boiler by adding 1-2 inches of water to the bottom of a medium saucepan. Set a glass or metal bowl on the top of the pan, ensuring that the bowl doesn't touch the water. Bring the water to a boil, then reduce it to a simmer.
Crack 3 large eggs into the double boiler boil, and beat with a whisk. Continue whisking the eggs over the double boiler until the temperature reaches 140°F. Be careful that the eggs aren't getting too hot, or they will cook. (I like to turn the stove off when the eggs reach about 125-130°F as the temperature will continue to rise due to the hot water in the pot).
Carefully remove the bowl from the saucepan and pour the eggs into a cool bowl or airtight container. Transfer the eggs to the fridge to chill while you start mixing up the cake (start on step 1 of the Chocolate Cake section of instructions now).
Wash out the bowl you used to pasteurize the eggs, set it overtop the saucepan again and bring the water to a simmer again. Add 3 ounces unsweetened baking chocolate to the bowl, making sure not to get any water in it. Keep the chocolate in the double boiler, stirring often, until it's completely melted, about 3-4 minutes. Carefully remove the bowl from the saucepan and set it aside to let the chocolate cool slightly (don't let it harden again).
Add 1 cup plus 2 Tablespoons granulated sugar to the bowl of your food processor and grind until fine and powdery.
Add 3/4 cup unsalted butter and the superfine sugar to the bowl of a stand mixer that with a paddle mixer attached. Beat the butter and sugar together until it's pale and fluffy, about 3 minutes.
Add the cooled melted chocolate and 1 teaspoon vanilla extract to the bowl with the butter and sugar. Beat again until combined, about 1-2 minutes. Scrape down the sides of the bowl. Switch the mixer attachment to the whisk.
Add 1/4 of the pasteurized egg to the bowl, and beat at high speed for 5 minutes. Scrape down the sides of the bowl completely. Repeat this 3 more times with the remaining egg, making sure that you scrape down the bowl before each addition of egg, and also any time you see that there is any frosting that's not mixing properly.
After all of the egg has been added, the frosting will be very soft. Place the whole bowl (with the whisk attachment) into the fridge for 30 minutes, beating on high speed for 1-2 minutes every 10 minutes. (Switch to step 6 of the Chocolate Cake section of the instructions).
Chocolate Cake
Heat oven to 350°F. Get out a 9x13" baking pan, and set it aside (there is no need to grease it).
In a large bowl, whisk together 3 cups all-purpose flour, 2 cups granulated sugar, 6 Tablespoons cocoa powder, 2 teaspoons baking powder, 2 teaspoons baking soda, and 1 teaspoon table salt.
Using the back of a spoon or a small measuring cup, make 3 indents into the flour mixture. Pour 6 Tablespoons canola oil or other neutral-flavored cooking oil, 2 Tablespoons white vinegar, and 2 teaspoons vanilla extract into each of the indents.
In a measuring cup, dissolve 2 teaspoons instant coffee (if using) into 2 cups lukewarm water. Pour this mixture over the mixture in the large bowl, and mix with a spatula until no dry bits remain.
Spread the batter into the baking pan and bake for 35 minutes, or until a toothpick comes out with just a few crumbs clinging to it. Cool cake completely on a cooling rack before frosting. While the cake is baking/cooling, complete the rest of the frosting. (Move back to step 4 of the French Silk Frosting section of the instructions).
Frost the cake right in the pan. If you want it to look similar to a store-bought Deep'n Delicious cake, fit a large piping bag with an open star tip (I used a Wilton #21) and pipe stars in even rows onto the cake. Top with chocolate sprinkles if desired.
Serve at room temperature. If you need to store the cake (or leftovers) for an extended time, cover it with plastic and put it in the fridge. Take the cake out to allow it to come to room temperature for at least 30 minutes before serving.
Notes
Note: If you buy pasteurized eggs from the store, you can skip pasteurizing them at home. Start the recipe at step 4 of the French Silk Forsting section of instructions.If you use storebought superfine or caster sugar, you can skip step 4 of the French Silk Frosting section of instructions.