Preheat oven to 350 degrees Fahrenheit. Line the bottom of three six-inch cake pans with parchment paper, then butter and flour the pans.
Combine flour, cocoa powder, espresso powder, baking soda, baking powder, and salt in a medium size bowl.
In the bowl of a stand mixer, beat the oil and sugars together.
Add the egg, then the egg yolks one at a time, beating until combined after each addition.
Scrape down the sides and add vanilla, mix to combine.
Alternate adding 1/3 of the flour mixture and 1/2 of the buttermilk, starting and ending with the flour. You will have three additions of flour and two additions of buttermilk. Scrape down the sides as needed and mix until incorporated after each addition.
Add the hot water and mix until just combined with a rubber spatula.
Distribute the batter evenly among the three prepared cake pans. Tap each pan gently on the counter to remove extra air bubbles.
Place cake pans in the oven on the middle rack and bake for 35-38 minutes, or until a toothpick inserted into the center of the cake comes out with just a few moist crumbs attached.
Remove cakes from oven and let cool in pans for about 15 minutes. Then, turn layers out onto a wire rack and let cool completely.
Beat softened butter and peanut butter with a hand beater, or the paddle attachment of a stand mixer, until smooth.
Gradually add powdered sugar, with the mixer on low, until combined.
Add vanilla, beat until incorporated.
Add heavy cream, one tablespoon at a time, again beating until incorporated.
Adjust to reach desired consistency by adding more powdered sugar or cream as needed.
Beat on high speed until smooth.
Once cakes are cool, level each layer by using a sharp serrated knife to cut off the rounded domes.
Roughly chop about 1/2 cup of mini peanut butter cups for the filling.
Place bottom cake layer on a cake board, using a small amount of frosting to keep it in place.
Spread a thin layer of frosting on top of the cake, then pipe a dam of peanut butter frosting around the edge of the cake layer using a pastry bag fitted with a large round piping tip.
Fill the center with half of the chopped peanut butter cups.
Spread a small amount of frosting on top of the peanut butter cups to help the next layer stick.
Stack second cake layer on top. and repeat steps 4-6.
Stack third cake layer on top, upside down, so that the bottom of the cake layer forms the top of the cake.
Give the cake a crumb coat of peanut butter frosting and place in fridge for 20 minutes.
Finish frosting the cake with the peanut butter frosting. Reserve extra frosting for piping on top of cake if desired.
Return the cake to the fridge for about 20 minutes.
While cake is chilling, place chocolate chips in a small heatproof bowl.
Combine heavy cream and butter in a small saucepan over medium heat, stirring frequently, until butter is melted completely and mixture is heated through. Do not let the mixture boil, but you will see bubbles start to form at the edges when it's ready.
Pour cream mixture over the chocolate chips and let stand for 5 minutes.
Stir until smooth, and let cool for a few minutes until it drips fluidly, but slowly off a spoon.
Remove cake from fridge and carefully spoon the ganache around the edges of the cake, pushing it over the edges so that it falls in drips down the side. Work all the way around the edge of the cake before filling in the middle.
Spoon or pour the ganache in the middle of the cake and carefully spread it outward so that it smooths together with your outer edge of ganache.
Return the cake to the fridge until ganache hardens.
Decorate as desired. I used a large open star tip to pipe large swirls of peanut butter frosting around the edge of the cake, then topped each swirl with a mini peanut butter cup.
*You can make your own buttermilk by measuring a scant 3/4 cup of milk (whole or 2%) and adding about 2 teaspoons of lemon juice or vinegar. Stir, and let sit for about 5 minutes before adding to the cake.