Preheat oven 350 degrees F. Grease and flour three 6” cake pans. Set aside
Brew a fresh pot of coffee. Keep coffee hot while cake is prepared.
In a large bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugars on medium speed for 4 minutes. Drizzle in the oil and mix 1 more minute.
Add eggs one at a time, scraping the bowl after each egg addition. Add vanilla and mix until just combined.
In a separate bowl, using a fine mesh sieve, sift the flour, baking soda and salt. Spoon and level the flours for an accurate measurement.
Whisk together the hot coffee, cocoa powder, 1 teaspoon espresso powder and buttermilk until the mixture is smooth.
Alternating between the dry ingredients and the coffee mixture, add a third of the dry ingredients into the mixing bowl on low speed. Immediately follow with half of the coffee mixture, followed by another third of the dry ingredients and the second half of the coffee mixture. Finish with the remaining dry ingredients, and mix until incorporated. Scrape bowl as needed,
Pour batter evenly into the prepared pans. Bake for 20 minutes are until a toothpick inserted comes out clean, Allow cakes to cool for 10 minutes before inverted the cakes on a wire rack to finish cooling.
To make the espresso buttercream, with an electric mixer fitted with the paddle attachment, mix the cream cheese and butter on medium speed until there are no lumps, and the consistency is smooth.
Add sifted powdered sugar to the bowl, 1 cup at a time, mixing first on low speed to prevent splashing, then turning the mixer to medium-low until incorporated. Repeat process with remaining 2 cups of powdered sugar. Add coffee liqueur and remaining espresso powder. Briefly mix one more time to complete the icing.
To decorate the cake, place one cake layer on desired serving platter. Place a large dollop of buttercream on the cake and spread evenly. Repeat process with remaining layers. Once the cake is stacked, use remaining buttercream to decorate the sides and top of the cake. Decorate with buttercream swirls or chocolate curls.