Step 1Heat the oven to 350 degrees. Grease and lightly flour a 9-inch round cake pan, or grease a 9-inch springform pan, line the bottom with parchment or wax paper, grease again and flour lightly.
Step 2Lightly combine the yolks, 3 tablespoons of buttermilk and the vanilla.
Step 3In a large mixing bowl, combine the flour, sugar, baking powder and salt and mix on low speed for 30 seconds to blend. Add the butter and remaining buttermilk. Mix on low until the dry ingredients are moistened. Increase the speed to medium (high speed if using a hand mixer) and beat 1 1/2 minutes to aerate and develop the cake's structure. Scrape down the sides. Gradually add the egg mixture in 3 batches, beating for 20 seconds after each addition to incorporate the ingredients and strengthen the structure. Scrape down the sides.
Step 4Scrape the batter into the pan and smooth the surface with a spatula. The pan will be about half full. Bake until a tester inserted near the center comes out clean and the cake springs back when pressed in the center, 30 to 40 minutes. The cake should start to shrink from the sides of the pan only after removal from the oven.
Step 5Let the cake cool in the pan on a rack for 10 minutes. Loosen the sides with a small metal spatula and invert onto a greased wire rack. To prevent splitting, re-invert so that the top is up and cool completely before wrapping airtight.