Preheat the oven to 350°F / 175°C. Line and grease three 8” pans or four 7” pans with parchment rounds. You can also use this recipe to make 4, 6-inch cake layers but the bake time will be a few minutes longer. If you don't have 4 cake pans, the batter can sit at room temperature for a few hours. Bake as many layers at a time as you can at a time.
Whisk together 3 cups cake flour, 3 cups sugar, 2 1/2 tsp baking powder, and 1 tsp salt in the bowl of a stand mixer or a large bowl.
Mix in 1 cup of room-temperature butter slowly with a paddle attachment 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.
Add in 1 1/2 cups sour cream, 2 Tbsp oil, and 1 tsp vanilla extract. Mix on a low speed until the batter is smooth.
Scrape down the sides and bottom of the bowl with a spatula, then beat on a medium speed for 30 more seconds to make sure everything is properly combined.
Divide the batter evenly between the prepared cake pans and bake for 33-36 minutes or until a toothpick comes out with a few moist crumbs. Let the pans cool for 10 minutes, then run an offset spatula around the perimeter of the pan to separate the cake from the pan. Place cake layers on a wire rack to finish cooling.
Place the cake pans 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. Set aside.