Beat ½ cup whole milk, 4 yolks, and 1 ½ teaspoons vanilla together with a fork in a 2-cup liquid measuring cup. Using stand mixer fitted with paddle, mix 1 ¼ cup plus, 5 oz. cake flour, 1 cup plus, 7 ounces sugar, 1 ½ teaspoons baking powder, and ½ teaspoon salt on low speed until combined, about 5 seconds. Add the 12 Tablespoons butter, 1 piece at a time, and mix until only pea-size pieces remain, about 1 minute. Add half the milk mixture, increase speed to medium-high, and beat until light and fluffy, about 1 minute. Reduce speed to medium-low, add remaining milk mixture, and beat until incorporated, about 30 seconds (mixture may look curdled). Give batter a final stir by hand. Divide batter evenly between prepared pans and spread into even layer using small offset spatula.