Preheat oven to 350°.
Grease and flour 2-9" round cake pans. Placing a piece of parchment paper, cut to fit bottom of pan before greasing will help removal of cake after baking.
Using the paddle attachment on athe stand mixer, beat butter and sugar at medium speed until mixture is light and fluffy. This should take 3-4 minutes. Stop to scrape sides of bowl frequently.
Add eggs and egg yolks, one at a time, mixing after each until combined.
Mix in vanilla extract.
In separate bowl, combine flour, baking powder and salt.
In a separate large mixing bowl, with your mixer on low, gradually alternate, adding flour mixture and egg/butter mixture, starting and ending with dry mixture until all is combined.
Divide batter between the two prepared pans.
Bake on center rack of the preheated oven for approx. 25-35 minutes, until a toothpick inserted in center comes out clean. Cool on wire rack, then remove from pans.