Preheat oven to 350 degrees F and place oven rack in the center of the oven. Butter, or spray with a non stick vegetable spray three 9 inch cake pans. Line the bottoms of the pans with parchment paper and set the pans aside. Dust off your abuela's cafetera and make yourself some Cuban coffee. Once you have brewed 1 cup worth of Cuban coffee and set aside
In a large bowl whisk together the sugar, flour, cocoa powder, baking powder, baking soda, and salt. In another bowl, whisk together the eggs, coffee, liqueur, buttermilk, melted butter, and vanilla paste. Once combined, mix in the dry ingredients slowly.
Divide the batter between the 3 pans as evenly as possible and bake for 22 minutes or until all pans pass the toothpick test. Once cooked, remove from the oven and allow the cakes to rest for about 10 minutes atleast. Then, remove the cakes from their pans and place them face down on parchment paper lined wire rack to cool completely.
Cakes must be completely cooled before frosting, otherwise your frosting will melt and you'll have a hell of a mess. You can also wrap them in plastic wrap once completely cooled if you're baking these ahead of time, they'll keep in your fridge for a few days until you're read to make your cake.
Now that your cakes are cooling, it's time to make your frosting. Temper your chocolate over medium heat. When the chocolate is completely melted, remove from heat and set aside. I know the chocolate is all shiny, melted and calling your name, tempting you to bust out the ice cream and eat it as is, but you can't do this. Ok ok, maybe just a spoonful, BUT THAT'S IT!
In a large sized bowl using your hand mixer, beat the butter until smooth and creamy. Then, add the sugar and beat until it is light and fluffy. Mix in the vanilla extract and espresso. Slowly add the melted chocolate and beat on low speed until incorporated. Once mixed completely, crank up the speed on the mixer til the frosting is smooth.
During this time you can also make your fudge filling. in a microwave safe bowl, add your chocolate chips and melt them in the microwave until fully melted then add in your condensed milk and espresso and whisk til combine. Allow to cool (about 30 min) and set aside.
Now that your cakes have completely cooled off, your frosting and fudge are done, it's time to assemble your cake. Place one cake layer bottom side facing up on your serving plate and slowly peel away the parchment paper (or plastic wrap, this way the less even part of the cake is on the bottom and it's easier to spread the icing.
Scoop about ½ of fudge and place in the center of the cake, spreading it out as evenly as possible. Allow about a ½ inch space around the edge so the filling doesn't "bleed" out onto the sides. You can also pipe some of your frosting along the outer edge to create a dam in order to prevent and "bleeding."
Gently, place the second layer of cake bottom side facing up on top of the icing and add the remaining fudge and spread it carefully. Repeating the same process as the previous layer. Finally place the third cake layer on top and begin spreading your buttercream through out the cake evenly. You can decorate with sprinkles or eat as is!