Preheat oven to 350°F/175°C. Line four 7-inch or three 8-inch cake pans with parchment rounds and grease with non-stick baking spray. Set aside.
Mix together 3 cups all-purpose flour, 1 cup granulated sugar, 2 cups brown sugar, 2 1/2 tsp baking powder, 2 tsp cinnamon, and 1 tsp salt with a stand mixer (with a paddle or whisk attachment) or hand mixer until fully combined.
Mix 1 cup of unsalted butter into the dry ingredients on a low speed. Continue to mix until no large chunks of butter remain, and the mixture looks crumbly.
Pour in 1 cup of egg whites and mix on low until incorporated.
Next, mix in 1 1/2 cups buttermilk, 2 Tbsp of vegetable oil, and 2 tsp of vanilla extract and mix on a low speed until fully incorporated. Scrape down the sides of the bowl with a rubber spatula, then beat on a medium speed for 30 seconds to make sure everything is properly mixed together.
Divide the batter evenly between the prepared pans. I like to use a digital scale to make sure each pan has the same amount of batter so that each cake layer is the same height.
Bake for 33-35 minutes or until a toothpick comes out with a few moist crumbs. Rotate the pans halfway through to help them bake evenly.
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 cake layers into the freezer for 30 minutes to accelerate the cooling process. Once the layers are cooled, carefully flip the pans and remove the layers.
Use a serrated knife to level the tops right before you plan to assemble your cake, or you can wrap and freeze them 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 your cake.