Preheat the oven to 350°F. Grease 2 9-inch cake pans. Cut out two pieces of parchment paper just the right size to fit in the bottoms of the pans. Insert the paper rounds and grease them as well.
In a medium bowl, stir together the flour, baking powder and salt. In another medium bowl beat the butter with an electric mixer until creamy, then add the sugar and continue to beat for 3 minutes until fluffy. Beat in the yolks one at a time, then beat in the whole eggs one at a time. Beat in the vanilla. Using a spoon or a rubber spatula add the flour mixture and the milk, in thirds, alternating between the milk and the dry ingredients. Stir just until well combined.
Divide the batter evenly between the pans and bake until a toothpick inserted in the middle of the cakes comes out clean, 22 to 27 minutes. Let the cakes cool in their pans on wire racks for 5 to 10 minutes, then flip them out of the pans and finish cooling them, right side up, on the wire racks.
When the cakes have cooled, spread the buttercream over the top of one of the cakes, place the second cake on top, and frost the whole cake with a very thin layer of frosting. Place the cake in the refrigerator for 15 minutes. Remove from the fridge (the buttercream should be hard – this is called the crumb layer, named because it seals in the crumb, and then when you add the next layer of frosting you won’t have little crumby flecks dotting the frosting. It will soften again when the cake comes to room temperature), and then spread the rest of the frosting over the top and sides of the cake.
If you are not frosting the cakes right away, you can wrap the two layers well with plastic wrap and keep them at room temperature for two to three days.This cake was adapted from Mark Bittman’s new book, How to Bake Everything. The man knows his way around a kitchen. And his daughter is in her 30s, so I can only assume he’s baked quite a few nostalgia-creamed cakes over the years. I wonder if he got as teary as me. I doubt it.