Preheat oven to 350°F / 175°C. Line four 7", three 8", or two 9" pans with parchment rounds and grease with nonstick spray. Set aside.
Mix 3 cups sugar, 2 1/4 cups all-purpose flour, 3/4 cup of cocoa powder, 2 1/2 tsp baking powder, and 1 tsp salt together in a stand mixer with a stand mixer and paddle attachment or hand mixer until fully combined.
Mix in 1 cup of room temperature, unsalted butter slowly into the dry ingredients 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. Mix in 1 1/2 cups of buttermilk in two installments, on a low speed.
Add in 2 Tbsp of vegetable oil, 2 tsp of vanilla extract, and 1 tsp instant espresso. 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 about a minute to make sure everything is properly mixed together. This also helps lighten the texture of the cake layers a bit.
Divide the batter evenly between your prepared pans. I like to use a scale to make sure each pan has the same amount of batter and will bake up to the same height.
Bake for 33-35 minutes or until a toothpick comes out with a few moist crumbs.
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 the cake layers into the freezer for 30 minutes to accelerate the cooling process. Once the layers are fully cooled, carefully flip the pans and remove the layers.
Use a serrated knife to level the tops of the layers right before you plan to assemble your cake, or you can wrap and freeze them in advance. They can also be wrapped tightly with plastic wrap and stored at room temperature for a few days.
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.