Preheat the oven to 350°F/177ºC. Prepare three 6-inch (15cm) or two 8-inch (20cm) cake pans by spraying the sides with cooking spray and fitting a parchment paper circle to the bottom of the pan.
Using a food processor, grind the pistachios into fine crumbs (see the photo above for a visual). You’ll still have about 1 and 1/2 cups of crumbs. Place 1 ¼ Cups (160g) of the pistachio crumbs into a medium bowl and set the rest of the crumbs aside in a smaller bowl to use as garnish on the decorated cake.
In the medium bowl with the pistachio crumbs, add the sifted cake flour, baking powder, baking soda, and salt. Whisk to combine and set aside.
In the bowl of your stand mixer fitted with the paddle attachment, beat the butter on high for two minutes until it’s light and creamy. Add the sugar and vegetable oil, then continue to mix on medium-high for another two minutes, scraping down the bowl and paddle as needed. Turn the mixer to low speed and add the egg whites one at a time, mixing until well combined. Add the sour cream, vanilla extract, and almond extract and mix for two minutes on high speed. Scrape down the bowl and paddle once more.
Turn the mixer to low and add in the dry ingredients all at once. When they’re just beginning to combine, add the green food coloring (if using) and the whole milk in a slow, steady stream. Continue to mix on low until incorporated, about 1 minute.
Pour the batter evenly into the prepared cake pans and bake for 28-32 minutes. They’re done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling.