In a bowl of a stand mixer or large bowl if you are using a hand mixer, beat the eggs on medium speed until pale yellow (3 to 5 minutes).
3 eggs, at room temperature
Add the sugar and beat for a couple of minutes.
3 cups (600 grams) granulated sugar
Add the cooled chocolate and mix, then add the coffee, buttermilk, oil, and vanilla.
3 ounces semisweet chocolate, melted and cooled to touch, 1½ cups brewed coffee, cooled, ¾ cup neutral vegetable oil, 1 tsp vanilla, 1½ cup buttermilk
Add the dry ingredients and combine on low speed for 1 minute or by hand until just combined. If you are using a stand mixer, be careful because you might end up with cocoa mixture everywhere!
Divide the batter equally into the prepared pans. Before putting them in the oven, thwack them gingerly on the countertop once or twice to remove any air bubbles.
Bake for about 60 minutes, until a toothpick inserted into the center comes out clean and the edges are just starting to pull away from the side of the pan.
Cool the cake layers in the pan. You may need to run a spatula or knife around the edge of the cake pans to get the layers to release (see notes).
Peanut butter cream cheese frosting
Put the cream cheese, butter, and peanut butter in the stand mixer or medium bowl if using a hand mixer, and beat until well combined (3 to 5 minutes).
1 cup (8 ounces) cream cheese, softened, ½ cup (1 stick, 4 ounces) unsalted butter, softened, ½ cup peanut butter
Add the vanilla and beat until combined.
1 teaspoon vanilla
Add the confectioners sugar and beat, scraping down the bowl as necessary. If you want a sweeter frosting, or if you want a thicker consistency (particularly if it is very warm where you are), add more sugar by a cupful at a time.
2 cups (8oz) confectioners sugar
To frost, place one cake layer right side up on a cake stand or plate. Use 1/2 cup of frosting and spread it into a thin layer. Carefully place the second layer right side up on top and repeat.
Place the third layer right side up on top. If you want to make a crumb layer so that cake crumbs don't appear on the outside of your cake (see note), spread a thin layer of frosting and then put the cake in the fridge. Otherwise use the remaining frosting to coat the cake, making the frosting (esp the sides) as smooth as possible.
Put the cake in the refrigerator while making the ganache.
Peanut butter chocolate ganache
Melt the chocolate in a double boiler or in a small metal bowl over a pot of slightly simmering water.
9 ounces semisweet chocolate, melted
In a small pot, heat the cream and peanut butter over low heat until the peanut butter has dissolved into the cream and the mixture is just starting to simmer.
½ cup heavy cream, ¼ cup peanut butter
Add the cream and peanut butter to the chocolate and whisk until smooth and uniform. Let cool (see note).
When the ganache has cooled to a dripping consistency (see note), use a squeeze bottle or spoon to drip a layer around the top of the cake, letting the ganache drip down the cake side every inch or so.
Fill in the center of the cake with ganache and smooth the top, being careful not to push the ganache over the sides of the cake.
This cake, or portions of the cake, can be frozen. Just double-wrap large pieces of cake in plastic wrap and then place in a freezer bag. To defrost, unwrap the cake and leave at room temperature.