Step 1
Preheat the oven to 350 degrees F (175 degrees C). Spray three 8-inch round cake pans with cooking spray. Line each pan with a round piece of parchment paper and spray with cooking spray.
Step 2
Prepare the cake: pulse pistachios in a food processor until finely ground 10 to 15 pulses. Transfer 1 1/2 cups ground pistachios to a bowl with flour baking powder salt and baking soda; whisk until well combined and set aside. Place remaining ground pistachios about 1 1/3 cups in a bowl and reserve for finishing the cake.
Step 3
Beat butter and white sugar for cake in a stand mixer fitted with a paddle attachment on medium-high speed scraping down the sides as needed until light and fluffy about 3 minutes. Add egg whites and beat on high speed until combined about 2 minutes.
Step 4
Mix in sour cream vanilla extract and almond extract until combined about 1 minute. Add flour mixture in batches on low speed until completely incorporated about 2 minutes. Mix in milk and food coloring until just combined about 1 minute.
Step 5
Divide batter evenly among the prepared cake pans. Gently tap each pan on the countertop to spread and flatten batter.
Step 6
Bake in the preheated oven until a toothpick inserted into the center of each pan removes cleanly 22 to 24 minutes. Cool cakes in the pans for about 10 minutes. Run a table knife around the edges to loosen cakes then invert carefully onto a serving plate or cooling rack. Let cool completely about 30 minutes.
Step 7
While the cakes are cooling prepare buttercream: beat cream cheese and butter in a stand mixer fitted with a paddle attachment on medium-high speed until light and fluffy about 3 minutes. Mix in powdered sugar in 1/2-cup increments on medium-low speed allowing sugar to be completely incorporated before adding more until combined about 4 minutes. Mix in vanilla and food coloring on medium-high speed until light and fluffy about 2 minutes.
Step 8
Place one cake layer on a serving plate or cake stand. Top with 1 cup buttercream and 1 tablespoon ground pistachios and spread evenly over the surface using a spatula. Place second cake layer on top; top with 1 cup buttercream and 1 tablespoon ground pistachios and spread evenly over the surface. Place third cake layer on top and spread 1 cup buttercream evenly over the surface. Spread 2 cups buttercream evenly around sides of assembled cake and smooth with a spatula. Transfer cake to the refrigerator and chill for 30 minutes.
Step 9
Remove cake from the refrigerator and spread remaining buttercream over top and sides of cake until sides are smooth and top is billowy. Using a small offset spatula make a spiral pattern on top of the cake. Press remaining ground pistachios into sides of the cake.
Step 9
Slice and serve immediately or chill in an airtight container until ready to serve. If chilled allow cake to come to room temperature before serving.