Position a rack in the upper third of the oven and preheat to 350°F. Grease a 9×13-inch baking dish with butter (or use cooking spray).
Place a fine-mesh sieve over a large bowl and use it to sift in the flour, baking powder, baking soda, and salt.
Combine the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use a large bowl and a handheld mixer.) Beat on medium-high speed until pale yellow and fluffy, about 3 minutes. Scrape down the sides of the bowl with a spatula.
With the motor running, add the whole eggs and egg yolk, one at a time, until fully combined. Scrape down the sides of the bowl.
Add the sour cream and vanilla and beat until just combined.
Add the dry ingredients and buttermilk and mix until just combined, making sure not to overmix the batter.
Transfer the batter to the greased baking dish and smooth it into an even layer.
Bake until golden, or until a toothpick inserted into the center comes out clean, about 30 minutes. (My tip for a perfectly baked/never dry cake: Use a quick-read thermometer: the temperature in the center should read between 200℉ and 205℉.) Let the cake cool in the pan to room temperature.
Once cool, frost with this Chocolate Frosting, which is absolutely delightful, not too sweet, and conveniently uses some of the leftover buttermilk. Alternatively, you may use your frosting or icing of choice.
Notes
*No cake flour? No problem! You can turn all-purpose flour into cake flour. For every 1 cup of all-purpose flour, you'll need to remove 2 tablespoons of it, and then replace that with 2 tablespoons of cornstarch. For best results, sift the flour and cornstarch mixture together 2-3 times to ensure it is well-combined and aerated. So for this recipe, you'll need 2½ cups all-purpose flour, less 5 tablespoons, plus 5 tablespoons cornstarch. If measuring by weight, this will be 250g AP flour and 35g cornstarch. *Need a gluten-free cake: I made gluten-free cake flour for this recipe by starting with a cup-for-cup substitute and using the same method described above. Important note: When converting baked good recipes, I use the weight of regular flour (in this case, the cake flour, which is 114g per cup) instead of the weight of the gluten-free blend, which is usually much heavier and will create a denser cake. GF flours also take more time to absorb moisture, so I let the batter sit in the pan for 15-20 minutes prior to baking. This prevents a gritty texture. **No buttermilk? You can make a cheater version by adding 1 tablespoon of lemon juice or white vinegar to 1 cup of whole milk. Let it stand on the counter for 5 minutes until it looks slightly curdled and proceed with the recipe.Prep ahead option: The cake can be made up to 2 days in advance but must be thoroughly wrapped in plastic wrap and stored in an airtight container at room temperature to prevent it from drying out.Want to remove the cake to a platter and frost the sides? There will be enough of this Chocolate Frosting to do so. Simply line the pan with parchment paper, creasing well at the edges and corners. When the cake has completely cooled, use the parchment like a sling to carefully lift the cake from the pan.