Preheat oven to 350°F / 180°C and grease two 8-inch round cake pans.
In a large bowl, sift the dry ingredients, including the flour, sugar, cocoa powder, baking powder, baking soda, and salt. (But not the espresso powder). Whisk everything together.
In a separate bowl, combine all the wet ingredients, except the hot water, which includes the eggs, milk, sour cream, vegetable oil and vanilla. Whisk together lightly until it makes a homogeneous mixture.
Pour the wet ingredients into the dry and whisk until everything is combined and there are no lumps.
In a small bowl or a glass, combine the hot water with the espresso powder and mix until completely dissolved. Pour into the cake batter and mix until combined.
Divide the batter evenly between your two cake pans and bake for 30-35 minutes, or until a skewer inserted comes out clean.
Let the cakes cool in the pan for at least an hour before removing them. Let them cool on a wire rack completely before filling and frosting.
Make the Chocolate Fudge Frosting
Chop the chocolate finely and put it into a medium-sized bowl.
Heat the cream in a saucepan on medium heat until it is scalding hot (just starting to see tiny bubbles form on the surface). Do not let it boil.
Pour the hot cream over the chocolate and let it sit for a minute, then stir to mix together and melt the chocolate. It should make a smooth, shiny ganache.
In a stand mixer or with an electric whisk, whip the butter on medium-high speed for 5 minutes.
Check the temperature of the chocolate ganache with your finger, it should have come down to room temperature by now. If it feels even slightly warm, wait 10 minutes and then check again. If you use it while it's warm, it will melt the butter. If it's at room temperature, turn your mixer back on at a low speed and slowly incorporate the chocolate ganache, 1 tablespoon at a time, mixing for a few minutes in between additions.
Once all the chocolate ganache has been incorporated, add powdered sugar, cocoa powder, vanilla, and salt. Switch to a paddle attachment on your mixer and mix everything in, slowly at first, then faster, beating for about 2 minutes.
Assemble the Chocolate Fudge Cake
Once the chocolate cakes have completely cooled, use a cake leveler or serrated knife to cut any domes off the top of the cake. If you want 4 thinner layers of cake, like I have in the pictures above, cut each cake in half horizontally as well to create 4 thin layers of chocolate cake.
Place your first layer of cake on top of a cake board or serving plate and top with a generous helping of the chocolate fudge frosting. Use an offset spatula to spread it out evenly.
Repeat with each of the layers. Once you have the top layer of cake on, spread a thin coating of frosting all over the top and sides of the cake to lock in crumbs, chill in the fridge for 10 minutes.
Add a thicker coating of frosting all over the cake and decorate however you like.
Notes
Tip: To get super even layers of cake and frosting I recommend using a cake leveler to measure and slice your cake layers and an ice cream scoop to measure out the same amount of frosting in between each layer. Note: This chocolate cake batter is very liquid, so I don't recommend using loose-bottomed cake pans to make this cake. I made this mistake when testing it and ended up with burnt cake batter all over the bottom of my oven! Use regular round cake pans and make sure you grease them well. I also like to line my cake pans with parchment circles to help them release more easily. If you have any problems with your buttercream, see my FAQ and troubleshooting section in the post above.