To make the cake: Preheat oven to 350 degrees F. Butter and flour three 6-inch cake pans or two 8-inch cake pans. This batter is sticky so I also lined the bottoms with parchment. I highly recommend this. You don’t want to bake the whole thing up and have it stick. Set the pans aside. See below for link as to how to bake cake layers flat. I do this every single time and it’s SO helpful. Also, I own only two 6-inch cake pans and I baked up the first two layers first and then the third last. The batter was a-ok to do this!
In a large bowl or the bowl of a stand-up mixer (with the paddle attachment), add the all-purpose flour, sugar, cocoa powder, espresso powder, baking soda, baking powder and salt. Mix until combined. Next, crack in the egg and egg yolk, pour in the buttermilk, warm water, olive oil and vanilla. Mix until thoroughly combined and the batter is smooth, about 1 minute. The batter will be thinner than cake batter that you’re probably used to—that’s ok!
Divide the cake batter amongst the cake pans and transfer to the oven to bake for 27 to 30 minutes, or until a skewer inserted into the center comes out clean. Clean out the bowl you used to make the cake and dry it thoroughly. While the cakes are cooling, make the frosting.
To make the frosting: In large metal bowl, whisk together the water, sugar, egg whites, cream of tartar, and salt. Set bowl over pan of barely simmering water and mix with handheld electric mixer at low speed. Gradually increase speed to high, beating until mixture holds stiff peaks, about 5 minutes.
Transfer bowl from pan to folded kitchen towel on counter and continue beating until mixture is cool and billowy, about 2 minutes more. Beat in vanilla. (Frosting can be made 4 hours ahead and chilled, covered.)
To make the coconut topping: Add the coconut flakes and red food coloring to a bowl. (I ended up covering my hands with a ziplock bag so I wouldn’t get food coloring all over my hands.) Mix the coconut flakes and red food coloring together until evenly distributed. I liked mine to be baby pink. If you want bright pink, you may need to buy neon food coloring.
To assemble the cake: Add a few tablespoons of frosting to the center of one of the rounds of cake. Smooth it around, until it reaches the edges. Place the second layer on top. And then place another few tablespoons of frosting to the center of the second round of cake. Smooth it around. Add the third layer. Add more frosting the top and the sides, smoothing it out the best you can. (Since we’re adding coconut flakes, it doesn’t have to be perfect.)
Press the coconut flakes to the sides, going all the way around. And add coconut flakes to the top of the cake. Slice and serve.