Preheat the oven to 350 degrees F. Butter and flour two 9-inch cake pans. In a small bowl, whisk together the flour, cocoa, baking powder, soda and salt.
In the bowl of your electric mixer, beat the eggs, sugar and oil together until combined, mixing on medium speed for about 2 to 3 minutes. Stir in the milk, vanilla extract and paste. With the mixer on low speed, stir in the dry ingredients, and once they are all added, increase the speed to medium-high. Beat the cake batter for another 2 to 3 minutes. Pour the hot coffee into the batter and stir by hand to incorporate it – it will seem a bit thin and water, but stir and fold the batter until it is combined. Pour the cake batter evenly into both pans. Place in the oven and bake for 30 to 35 minutes, or until the center is set. Let the cake cool almost completely (I wait about 25 minutes) before gently turning it out on parchment paper. This cake is super moist and soft, so be careful!
I like to wrap the cakes in plastic wrap once cool and refrigerate or freeze so they are easier to frost. I freeze them overnight. Then I make the frosting the next morning and go from there. To frost, remove the cakes and place a layer of the chocolate fudge frosting on one of the cakes. Top it with a big spoonful of the cocoa frosting and even it out with a spatula or spoon. Place the other cake layer on top.
For the multiple frostings on the outside, I start at the bottom and using a knife, place big scoops of the frosting onto the bottom of the cake, all around. I then do the same with the cocoa frosting. Finally, I do the same with the vanilla, place it on top and down the top edge. It looks messy! (See photo above.) Using an offset spatula or knife, start dragging it around the cake so all of the frosting smoothes out at once. I do this multiple times, using multiple spatulas (or just washing the one I have) until it looks smooth enough to my liking. It’s supposed to look messy and like the colors are run together.
If desired, finish it off by topping with some chocolate curls. To do this, I simply stick a chocolate bar in the freezer for an hour or so, then use a vegetable peeler to “peel” some curls.