Set a rack in the middle of the oven and preheat to 350 degrees F. Very lightly grease the bottom of two 8-inch cake pans (do not grease the sides) and top with parchment rounds. Place the pans on a baking sheet, if possible (this will make taking both cakes in and out of the oven at once easier).
In a medium bowl, thoroughly whisk together the flour, cocoa powder, baking powder and salt. In a liquid measuring cup, combine the half-and-half, coffee and vanilla. Crack the eggs into a small bowl or liquid measuring cup.
In a stand mixer fitted with the paddle attachment, combine the butter and sugar on low speed for 3 minutes until pale and fluffy. If there are any bits of unincorporated sugar and/or butter on the sides or bottom of the bowl, use a spatula to incorporate them and mix for an additional 30 seconds.
Add the eggs slowly, one at a time, stopping to scrape down the bowl all the way to the bottom after the second and final egg. The batter may begin to look slightly broken by the end of this step; it’s ok.
On medium speed, swiftly alternate between adding the dry and wet ingredients, starting and ending with the dry. This shouldn’t take longer than a minute.
Turn off the mixer and scrape down the bowl, all the way to the bottom, making sure there are no hidden dry patches. Turn the speed up to medium and beat for an additional 30 seconds to aerate the batter. Do not skip this step.
Divide the cake batter evenly into the prepared pans. Use an offset spatula to even out the tops, ensuring the cake rises evenly.
Bake for 28-30 minutes, or until a toothpick comes out clean from the center. Cool to room temperature before removing from the pan. Run an offset spatula or knife around the edges to help release the sides of the cake from the pan, then place a cardboard round or large cutting board against the cake pan and gently flip.
Prepare the Buttercream:
Place the sugar and water in a medium-sized saucepan (do not stir). Cover and turn the heat to high. Once the liquid begins to simmer and steam develops, remove the cover (this helps prevent crystallization). Using a digital or candy thermometer, cook the sugar to the soft boil stage, 235-245 degrees F.
While the sugar is cooking, whisk the eggs on high in a stand mixer fitted with the whisk attachment, until a soft peak has formed (for a more stable meringue, start the eggs on a lower speed and slowly turn the mixer up to high once the whites are frothy).
Turn the mixer speed down to medium-low and very slowly pour the syrup down the side of the bowl into the egg whites (this will “cook” the egg whites, making them safe to consume. Don’t pour the hot syrup directly into the meringue or you’ll have scrambled egg whites.
Once the syrup is completely incorporated, turn the speed to high. The meringue will continue to form a stiff peak as it cools down. Mix on high until the meringue comes to room temperature, approximately 15-20 minutes.
Once at room temperature, slowly begin incorporating the soft butter on medium speed. Once all of the butter has been added, turn the mixer speed up to medium-high and slowly add the salt, vanilla, and peanut butter. Turn the speed back up to high at the end for about 30 seconds to fluffy up the buttercream.
Assemble the Cake:
Place the first layer of cake on a revolving cake stand, removing the parchment paper. Placing a cardboard round below the cake is optional but will make transporting the cake easier after it is assembled.
Spread approximately one cup of buttercream on the cake and spread it around evenly with an offset spatula. Add more buttercream as needed to reached the desired thickness.
Place the second layer on top, evening it out with the first. Use an offset spatula to apply a thin layer of frosting to the side and top of the cake. Chill in the refrigerator for 30 minutes to set this first layer of buttercream. Cover the entire cake with a final layer of frosting. Grate some unsweetened or semi-sweet chocolate on top of the cake for decoration, if desired. (Ganache and/or chopped peanut butter cups would also be delicious on top).
The finished cake can be stored at room temperature for up to 3 days; no need to refrigerate. After that it can go in the refrigerator for a few more days, but serve it at room temperature for best flavor and texture.
Superfine sugar will result in a more moist, light cake (compared with standard granulated white sugar, which will create a more dense cake). If you don’t want to purchase it, pulse regular in the food processor several times until the texture becomes more fine.Please read my full post for a thorough list of recipe tips, including notes on ingredient and equipment substitutions.Make-Ahead: If you want to prepare this in advance, I recommend wrapping the cooled, unfrosted cakes in plastic wrap and then freezing them for up to two weeks. You can also freeze the buttercream. The cake can be frosted while frozen, but let the buttercream come to room temperature first.