Preheat your oven to 350º F. Prepare your baking pans by brushing them with butter and lightly flouring them. This ensures that your cake releases easily after baking.
In a large mixing bowl, cream together the unsalted butter and granulated sugar using an electric mixer until the mixture is light yellow and fluffy, which should take about 2 to 3 minutes. This step is crucial as it incorporates air, leading to a lighter cake.
Add the eggs one by one, ensuring each egg is fully mixed in before adding the next. This helps maintain the emulsion and keeps your batter smooth.
Next, mix in the egg yolks, continuing to beat until fully incorporated and the mixture is creamy.
In a separate bowl, whisk together the kosher salt, baking powder, and all-purpose flour. This helps distribute the leavening agent evenly throughout the flour for consistent results.
Gradually add half of the flour mixture to the butter and sugar mixture, stirring until just combined. This prevents overmixing, which can toughen the cake.
Now pour in half of the buttermilk and mix until combined. Repeat this process with the remaining flour and buttermilk, stirring gently after each addition.
Finally, add the vanilla extract and mix until everything is just combined. Avoid overmixing to ensure a tender cake.
Divide the batter evenly between the prepared pans or pour it all into a 9×13 baking dish. Smooth the top with a spatula.
Bake in the preheated oven until the cake springs back when touched and a toothpick inserted in the center comes out clean. For two 8-inch pans, this should take around 25 minutes; for two 9-inch pans, about 30 minutes; and for a 9×13 pan, about 35 minutes.
Once baked, remove the cakes from the oven and allow them to cool for about 8 to 10 minutes in the pans. Then, transfer them to a wire rack to cool completely before frosting.