Prepare pans: Brush two 9-inch by 2-inch round cake pans with butter and line with parchment. Brush the parchment with butter, and dust with flour.
Whisk together cake flour, baking powder, and salt in a large bowl.
Beat butter and both sugars in the large bowl of an electric mixer fitted with the paddle attachment on high until light and fluffy, about 6 minutes.
Beat in whole eggs and egg yolks, one at a time, until combined. Beat in vanilla extract.
With mixer on low, add flour mixture to butter mixture in 3 additions, alternating with buttermilk. Scrape down bowl as needed. Stir in mini chocolate chips.
Divide batter between prepared pans and bake until cake tester comes out clean, 40 to 45 minutes. Let cakes cool in pans 10 minutes, then unmold onto wire racks. Reinvert and allow cakes to cool completely, right side up.