Grease two 10 x 3 inch round pans. Preheat the oven to 350F. Have all ingredients at room temperature.
In the bowl of an electric mixer, beat at high speed until light and fluffy:
8 oz. (2 sticks) unsalted butter
2 cups sugar
Add and beat on medium speed until fluffy:
6 large egg yolks
1 ½ teaspoons pure vanilla extract
On a piece of wax paper, sift together:
3 ½ cups cake flour
1 tablespoon plus ½ teaspoon baking powder
¾ teaspoon salt
At low speed add the dry ingredients to the butter and egg mixture alternately with:
1 ½ cups milk
Pour 3 ½ cups of the batter into one prepared pan and the remaining batter into the other. Bake the less full pan for 20-25 minutes and the fuller pan for 30-35 minutes, or until a cake tester inserted into the center of the cake comes out clean. Cool the cakes on a wire rack for 15 to 20 minutes before turning them out of their pans.