Brown the Butter
Melt butter in a medium sized saucepan over medium heat.
Decrease heat to medium-low and cook, stirring and scraping the bottom with a heatproof spatula, until brown bits form on the bottom of the pan (butter will sizzle, foam, and pop then this will slow before it browns). Pour into a heatproof bowl and allow to cool until no longer warm to the touch before proceeding.
Make the Cake
Preheat oven to 350F (175C) and grease 3 8” (20cm) round baking pans with baking spray. Line the bottoms with rounds of parchment paper to ensure the cakes won’t stick.
In a large mixing bowl (or the bowl of a stand mixer), whisk together cake flour, sugar, baking powder, baking soda, and salt.
Add (cooled) browned butter and use an electric mixer to stir on low-speed until thoroughly incorporated.
In a separate, medium-sized bowl or large measuring cup, whisk together buttermilk, eggs, and extracts until well-combined.
With mixer on low-speed, gradually drizzle the buttermilk mixture into the flour mixture. Scrape the sides and bottom of the bowl to ensure the batter is uniform (it’s alright if you notice small lumps in the batter).
Add pistachios and use a spatula to stir until well incorporated.
Add drops of food coloring, if desired. Stir until uniform in color.
Evenly divide batter into prepared pans and bake in the center rack of 350F (175C) oven for 25 minutes or until a toothpick inserted in the center comes out clean or with moist crumbs.
Allow cakes to cool in their pans for 15 minutes before running a knife around the edge of the cake to loosen it from the pan then carefully invert onto a cooling rack to cool completely. Cakes must be completely cooled before decorating.
Assembly
Level cakes if needed (I linked to my favorite cake leveler in the “Equipment” section above) and decorate with frosting. I did a smooth, semi-naked covering for the sides of the cake with thicker frosting in between layers and on top of the cake, but you can completely cover the entire cake with a single batch of Swiss meringue buttercream. If desired, top cake with additional chopped pistachios.