Preheat the oven: Preheat to 350°F (177°C).
Prepare cake pans: Grease and flour two 9-inch round cake pans. Line the bottoms with parchment paper for easy removal.
Cream butter and sugar: In a stand mixer with the paddle attachment, beat butter and sugar on medium speed until light and fluffy, about 3–4 minutes. Scrape the bowl often.
Add eggs: Add eggs and egg yolks one at a time, mixing well after each addition.
Add vanilla: Mix in vanilla extract until incorporated.
Combine dry ingredients: In a separate bowl, whisk together cake flour, baking powder, and salt.
Mix everything together: With the mixer on low, alternate adding the dry ingredients and buttermilk to the butter mixture. Start and finish with the flour mixture, mixing just until combined.
Fill the pans: Divide the batter evenly between the prepared cake pans.
Bake the cakes: Bake 25–35 minutes, or until a toothpick inserted in the center comes out clean. Cool in the pans for 10 minutes, then transfer the cakes to a wire rack to cool completely.