1. Make the Cake

1. Prepare the Pans: Preheat your oven to 350°F (175°C). Grease and line three 8-inch round cake pans with parchment paper.
2. Mix the Dry Ingredients: In a large bowl, sift together the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Whisk to combine.
3. Combine Wet Ingredients: In a separate bowl, whisk together the eggs, buttermilk, vegetable oil, and vanilla extract. Slowly add the wet ingredients to the dry ingredients and mix until just combined.
4. Add the Coffee: Gradually stir in the hot coffee (or hot water). The batter will be thin, but this ensures a moist cake.
5. Bake the Layers: Divide the batter evenly among the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
6. Cool the Cakes: Allow the cakes to cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.

2. Make the Chocolate Pudding Filling

1. Combine Dry Ingredients: In a medium saucepan, whisk together the sugar, cornstarch, cocoa powder, and salt. Gradually whisk in the milk until smooth.
2. Cook the Pudding: Place the saucepan over medium heat and cook, whisking constantly, until the mixture thickens and starts to bubble, about 5-7 minutes.
3. Temper the Eggs: In a small bowl, whisk the egg yolks. Gradually add a small amount of the hot pudding mixture to the yolks, whisking constantly to prevent curdling. Then, return the yolk mixture to the saucepan and continue cooking for 1-2 minutes.
4. Add Chocolate and Butter: Remove the pudding from the heat and stir in the chopped chocolate, vanilla extract, and butter until smooth.
5. Chill the Pudding: Transfer the pudding to a bowl, cover with plastic wrap pressed directly against the surface to prevent a skin from forming, and refrigerate until completely cool, about 2 hours.

3. Assemble the Cake

1. Level the Layers: If needed, level the tops of the cake layers using a serrated knife. Crumble one layer into fine crumbs and set aside for decorating.
2. Layer the Cake: Place one cake layer on a serving plate or cake stand. Spread a generous layer of the chocolate pudding filling over the top. Add the second cake layer and spread more pudding on top.
3. Frost the Cake: Spread the remaining pudding over the top and sides of the cake, smoothing it evenly.
4. Add the Crumbs: Press the reserved cake crumbs onto the sides and top of the cake, covering it completely.

4. Chill and Serve

Refrigerate the assembled cake for at least 1 hour before serving to allow the layers to set. Slice and enjoy!