This is an insanely delicious, moist, rich, decadent piece of chocolate cake that just happens to include avocado!
Combine chocolate, cocoa powder and three tablespoons of coffee in a heat-proof bowl. (The best way to do this is the brew coffee and place 2 cups into a medium bowl. Remove 3 tablespoons. You will use the remainder in a moment.)
Place bowl over a pot of simmering water, gently stir until melted and combined. Remove from heat. (You can also melt in microwave. Heat for 30 seconds then switch to 10-second increments. Stir between each heating.)
In another bowl, whisk together the vegetable oil, remaining coffee, avocado,and both sugars. Stir in the slightly cooled chocolate.
Add the wet ingredients to the dry ingredients. Whisk until fully combined and smooth, scraping the side of the bowls completely. (try to not over mix)
Divide batter between both baking pans. Bake in preheated oven for 45 minutes, until a toothpick inserted into center of cake comes out clean.
In a the bowl of an electric stand mixer, fitted with whisk attachment whisk butter and sugar on medium high speed until very pale and fluffy or about five minutes.
Once all cream has been added and mixture is mostly combined, turn off the mixer and scrape down the sides of the bowl.
Now turn the mixer onto medium-high to high and whisk for 3-5 minutes or until mixture is lighter and fluffier. The frosting will be shiny and seem to have many large air bubbles throughout and this is exactly what we are going for. (You can smooth those out on the cake if so desired.)