Set the oven to 350°F (175°C). Grease a 9-inch round cake pan and dust it lightly with flour, or line it with parchment paper.
In a medium bowl, sift together the cake flour, baking powder, baking soda, and salt. Set aside. Using an electric mixer, beat the softened butter and granulated sugar until the mixture becomes light and fluffy, about 3 to 4 minutes.
Stir in the finely ground pistachios until fully mixed with the butter and sugar. Add the egg whites one by one, beating well after each addition until they are completely blended in. In another bowl, whisk together the buttermilk, sour cream, vanilla extract, and almond extract.
Add the dry ingredients to the butter mixture in three parts, alternating with the wet ingredients in two parts. Start and end with the dry ingredients. Mix gently and stop as soon as everything is combined to avoid over mixing.
Pour the batter into the prepared pan and smooth the surface. Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool completely on a wire rack.
For the frosting, beat together the softened butter and cream cheese until smooth and creamy. Gradually add the confectioners’ sugar and vanilla extract, beating until fluffy.
Once the cake has fully cooled, frost the top and sides evenly with the pistachio cream cheese frosting. Chill the cake for at least 30 minutes to help the frosting set before slicing and serving.