Preheat the oven to 350 degrees F (180 degrees C). Grease a 9 by 13-inch baking dish or two 9-inch cake pans.
Cream the Unsalted Butter (3/4 cup) and Granulated Sugar (2 cup) in an electric mixer with the paddle attachment until light and fluffy, about 5-7 minutes.
On medium speed, add the Vanilla Extract (1 tablespoon) and Large Egg (3) one at a time until fully incorporated. Batter will be nice and smooth!
Sift the All-Purpose Flour (1 3/4 cup), Baking Soda (1 teaspoon), and Kosher Salt (1 teaspoon) in a medium bowl.
In another bowl, whisk together the Water (2/3 cup), Unsweetened Cocoa Powder (2/3 cup), and Instant Espresso Powder (1 teaspoon). Add the Half and Half (2/3 cup), then whisk until smooth.
With the mixer on low, add the flour and chocolate mixes alternately in thirds, starting and ending with the flour. Scrape down the sides of bowl with a rubber spatula to be sure batter is incorporated.
Pour into prepared pans, smooth the top, and bake for 25-35 minutes, or until a cake tester comes out clean.
Place the Bittersweet Chocolate (12 ounce), Unsalted Butter (3 tablespoon), and Instant Espresso Powder (2 teaspoon) in a bowl.
Heat the Heavy Cream (1 1/4 cup) to a simmer and pour over the chocolate, stirring occasionally until melted. If the chocolate has not melted, zap in the microwave for a minute.
Stir in the Kahlua (1 tablespoon) and Vanilla Extract (1 teaspoon) and stir until smooth. Cover and refrigerate for 30 minutes only.
Scrape down the sides of the bowl and beat with a hand mixer until soft peaks form, about 20 seconds. Any longer the frosting may curdle, so be careful!
Once cake has cooled completely in the pan, turn it out onto a flat surface and frost the top with frosting if a sheet cake, or the middle, tops, and sides for a round cake. There will be plenty of frosting either way!
Decorate, serve and enjoy!