Preheat the oven to 350°F / 175°C. Grease then line three 8-inch cake pans with nonstick spray and parchment paper rounds. Set aside.
Pour 1 1/4 cups (160g) of finely chopped pistachios, 2 cups all-purpose flour, 3 cups granulated sugar, 2 1/2 tsp baking powder, and 1 tsp fine salt into a large bowl or the bowl of a stand mixer. Whisk together until combined.
Then mix 3/4 cup (1 1/2 sticks) of room temperature, unsalted butter slowly into the dry ingredients on a low speed. Continue to mix until no large chunks of butter remain and the mixture looks like moist sand.
Pour in 1 cup of egg whites and mix on low until just incorporated. The batter will be thick.
Next, mix in 1 1/2 cups of sour cream, 2 Tbsp of vegetable oil, 2 tsp of vanilla extract, and 1 tsp almond extract (optional) at a low speed until fully incorporated. If you want to amp up the color of the cake layers, add in 1/4 tsp of green gel food coloring.
Scrape down the sides of the bowl with a rubber spatula, then beat on a medium speed for about a minute to make sure everything is properly mixed together. This also helps lighten the texture of the cake layers a bit.
Divide the batter evenly between the prepared pans. I like to use a scale to make sure each pan has the same amount of batter and will bake up to the same height (about 600g per pan).
Bake for 33-36 minutes or until a toothpick inserted in the center of one of the layers comes out with a few moist crumbs. Let the pans cool for 10 minutes, then run a small offset spatula around the perimeter of the pan to separate the cake from the pan.
Place the cake layers into the freezer for 30 minutes to accelerate the cooling process. Once the layers are fully cooled, carefully flip the pans and remove the layers.
Use a serrated knife to level the tops of the layers right before you plan to assemble your cake, or you can wrap and freeze the layers if you're making them in advance. If you make these cake layers in advance and freeze them, let them thaw for about 20 minutes before making your cake. The cake layers should still be slightly cold to the touch, which will make it easier to assemble the cake.