The secret to the natural deep pink color and raspberry flavor in this buttercream is freeze-dried raspberries. I also use freeze-dried strawberries for an equally beautiful color and flavor. Rose water is a perfect pairing with red berries, and in this buttercream? Divine. The fluffy white cake sets off the pink buttercream here, which is the star of the show--so feel free to use your favorite white cake recipe (or *box*...I won't tell). I made a buttercream rose for the center of the cake following many random how-to videos. You can do that too, or decorate with more sprinkles in the center of the cake, or fresh raspberries. The cake can be made in advance and frozen until ready to use. The cake can be frosted and refrigerated a couple of days in advance of serving.
Preheat the oven to 350°F. Grease and flour two 9-inch cake pans.
In a medium bowl or large measuring cup, whisk the egg whites, whole egg, ¼ cup of the milk, and vanilla. Set this aside.
In the bowl of an electric mixer, whisk the dry ingredients until combined. Using the paddle attachment on low speed, add the butter one piece at a time until the mixture is a fine crumbly texture. This takes some time, but the fine crumb will happen with patience! Add the remaining milk and continue to mix on low for about five minutes, stopping to scrape down the sides of the bowl occasionally. Add the egg mixture in 3 separate batches, mixing on low until light and fluffy, another 3-5 minutes. Scrape and fold the batter to incorporate everything.
Scrape the batter evenly into the pans. Bake until the cake is spongy in the center when touched with the tip of your fingers, or until a cake tester comes out with a few crumbs when inserted in the center, about 30 minutes. Be very careful not to over-bake! Start checking at 20 minutes.
Let the cake rest for 10 minutes, loosen the sides from the pan with a knife, then shake to loosen the cake from the bottom of the pan. Flip the cakes out carefully onto plates or other flat surface.
To make the raspberry powder, process the freeze-dried raspberries in the food processor until pulverized. Sift twice through a fine mesh sieve to remove the seeds.
In an electric mixer fitted with the paddle attachment beat the butter until it is smooth. Add the raspberry powder and beat on low speed, scraping down the sides of the bowl to get it all incorporated. Add the confectioners’ sugar in several batches (to avoid a big poof when you turn on the mixer) and mix on low to incorporate. Add the rose water, and then add a tablespoon of milk as you add the confectioner's sugar—but only enough milk to make the buttercream smooth; be careful not to add too much liquid. The buttercream should be thick but spreadable.
Slice the cake layers in half crosswise to make four layers; we're using three layers for this cake, so set one layer aside for another use (wrap well and freeze for later!).
Place one layer of the cake with the flattest side down so the cake will sit evenly. Coat the top with about 2/3 cup of the buttercream. Repeat this with a second layer. For the top layer, make sure the flattest side face up. Coat the exterior of the cake with buttercream. Smooth the sides and top.
Decorate the cake with sprinkles, buttercream roses, or raspberries.