Preheat the oven to 350°F. Prepare three 6-inch cake pans or two 9-inch cake pans by spraying the sides with a cooking spray (Baker's Joy is my favorite) and a wax paper circle fitted to the bottom of the pan. Alternatively, you can grease and lightly flour the pans.
Sift the cake flour and then measure by spooning and leveling it in your measuring cup. Add the cake flour, baking powder, baking soda, and salt into a bowl and whisk to combine. Set aside.
In the bowl of your stand mixer (a handheld mixer works fine too!), cream the butter for on high for two minutes until it's light and fluffy. Add vegetable oil and sugar, then continue to mix on med-high for another two minutes. Add the whole eggs and egg yolk one at a time, mixing thoroughly after each addition. Add vanilla and sour cream and mix for one minute on high, scraping down the bowl and paddle once more.
With the mixer on low speed, add in the dry ingredients and mix until just combined. Add the milk slowly and mix until just incorporated. Scrape down the sides and bottom of the bowl and give it a few stirs to make sure there are no lumps (without over-mixing). The batter will be slightly thick, but pourable.
Pour batter evenly into prepared cake pans (no more than ⅔ of the way full) and bake for 30-35 minutes. They're done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they're entirely room temperature before applying any frosting.
In a stand mixer fitted with a paddle attachment, whip butter on medium speed until creamy and light in color, about four minutes. Scrape down the bowl and paddle and turn the mixer to low, then add powdered sugar, cocoa powder, milk, salt, and vanilla extract. Increase the speed to medium and beat for two full minutes.
Once the cakes have cooled, torte them before filling and frosting with chocolate buttercream. To create the design pictured, use an icing scraper to smooth the sides and make them straight, then gently drag a cake comb through the buttercream to create lined texture. Use Wilton Tip 1M to create a rope border around the top edge by piping overlapping rosettes. Add rainbow sprinkles to finish the look!
