Preheat your oven to 350°F (175°C). Grease and line the bottoms of three 8-inch round cake pans with parchment paper. Lightly grease the parchment.

In the bowl of a stand mixer or a large bowl, sift together the flour, sugar, cocoa powder, baking soda, baking powder, and salt. Mix on low for 30 seconds to combine.

In a separate bowl, whisk together the eggs, buttermilk, oil, and vanilla until smooth. With the mixer on low speed, slowly pour the wet ingredients into the dry. Mix just until combined—the batter will be thick.

Carefully pour in the hot coffee. The batter will be very thin; this is correct. Mix on low until just combined, scraping the bottom and sides of the bowl as needed.

Divide the batter evenly among the prepared pans. Bake for 22-26 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.

Let the cakes cool in their pans on a wire rack for 15 minutes. Then, carefully run a knife around the edges and invert them onto the racks to cool completely.

Wrap cooled layers tightly in plastic wrap and freeze for 30 minutes for easier, crumb-free frosting.

In a medium saucepan, heat the milk over medium heat until it just begins to steam. Do not boil.

In a separate bowl, vigorously whisk the egg yolks, sugar, cornstarch, and salt until thick and pale yellow.

While whisking constantly, slowly drizzle about half of the hot milk into the egg yolk mixture to temper it. Then, pour the entire egg-milk mixture back into the saucepan with the remaining milk.

Cook over medium heat, whisking constantly, until the mixture becomes very thick and bubbles break the surface, about 2-3 minutes. Cook for 1 full additional minute to cook out the cornstarch taste.

Remove from heat. Immediately whisk in the chopped chocolate, butter, rum, and vanilla until completely smooth and glossy.

Press plastic wrap directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate for at least 2 hours, or until completely cold and set.

In the bowl of a stand mixer, beat the softened butter on medium-high speed until completely smooth and creamy, about 3 minutes.

With the mixer on low, gradually add the sifted confectioners’ sugar and cocoa powder. Mix until incorporated.

Add the cooled coffee, vanilla, and salt. Beat on medium-high speed for 3-4 minutes, scraping down the bowl as needed, until the frosting is very light, fluffy, and spreadable. If it’s too thick, add a teaspoon of milk or coffee. If too thin, add a bit more sugar.

If your cake layers have domed tops, use a long serrated knife to carefully slice them off to create flat, even surfaces.

Place one cake layer on your serving plate or cake stand. Spread half of the chilled chocolate-rum filling evenly over the top, leaving a small border.

Gently place the second cake layer on top. Spread with the remaining filling.

Top with the final cake layer.

Apply a thin layer of mocha buttercream over the entire cake to trap crumbs. Refrigerate for 20 minutes to set.

Frost the top and sides of the cake with the remaining buttercream using an offset spatula. Create swirls or smooth sides as desired.

Decorate with chocolate shavings and espresso beans. For best texture and flavor, let the cake sit at room temperature for about 30 minutes before slicing.