Preheat oven to 350°F. Line two 7-inch pans, one 6-inch pan, and two 4-inch pans with parchment rounds, and grease with non-stick cooking spray.
Mix together all dry ingredients (flour, baking powder, sugar, and salt) in a stand mixer with a paddle attachment until fully combined.
Mix chunks of room-temperature butter slowly into the dry mix, on a low speed. Continue to mix until no large chunks of butter remain, and the mixture becomes crumbly.
Pour in egg whites, and mix on low until just incorporated. Mix in the buttermilk in two installments, on a low speed.
Add in vanilla and oil, and mix at a low speed until fully incorporated. Scrape down the sides of the bowl with a spatula, then beat on low speed for about 15 seconds (the key is to mix until the ingredients are JUST incorporated, so that the batter isn't over mixed).
If desired, add in green gel food coloring. Mix the color in by hand using a rubber spatula, scraping the sides and bottom of the bowl part way through. Mix until the batter is evenly colored.
Divide batter between the prepared cake pans, filling each pan with the same height of batter.
Bake for 32-35 minutes, or until a toothpick comes out with a few moist crumbs. Allow the pans to cool for 10 minutes, then run an offset spatula around perimeter of the pan to separate the cake from the pan.
Place cake layers into the freezer for 45 minutes, to accelerate the cooling process. Once the layers are fully cooled, carefully flip the pans and remove the layers from the pans.
Use a serrated knife to level the tops of the layers, and then frost as desired.