Preheat your oven to 350F (175C) and prepare two 8-inch round cake pans by lining each of the bottoms with a round of parchment paper and generously spraying the sides with baking spray.
In a stand mixer (or you may use a large bowl and an electric mixer) stir together flour, sugar, baking powder, and salt until thoroughly combined.
Turn your mixer to low speed and add butter, one tablespoon at a time, not adding the next tablespoon until the first is incorporated. When you’re finished, the mixture should resemble coarse sandy crumbs.
Add oil and stir until combined.
In a measuring cup, whisk together milk, sour cream, and vanilla extract and stir into batter until thoroughly incorporated.
In a separate clean, dry, and grease-free bowl use clean beaters to beat egg whites to stiff peaks.
Use a spatula to gently fold egg whites into batter (don’t overmix, but make sure there are no lumps of egg white remaining).
Portion 3 cups of batter into a separate bowl (you’ll be left with 5 cups in your first bowl).
In a large measuring cup, stir together hot water and cocoa powder. Add sour cream and sugar and whisk until well combined, then stir into your smaller bowl of batter.
Dollop approximately ⅓ cup of white batter into the center of each of your prepared cake pans. Using a clean scoop, scoop just shy of ⅓ cup of chocolate batter and drop that directly onto the center of the white batter. Repeat, alternating batter flavors, until you have used all of the batter.
Carefully transfer pans to 350F (175C) oven and bake for 35-40 minutes or until a toothpick inserted in the center comes out clean or with moist crumbs.
Allow to cool in pans for 15 minutes then run a knife around the edges of the cake to loosen from the sides and carefully invert onto a cooling rack to cool completely.
If needed, carefully level the cakes with a sharp serrated knife once completely cooled.
Decorate using white chocolate icing or with your frosting of choice.
