4 large eggs, room temperature
½ cup whole milk, room temperature
2 teaspoons vanilla extract
2¼ cups sifted plain cake flour
1½ cups sugar
2 teaspoons baking powder
¾ teaspoon salt
½ pound (2 sticks) unsalted butter, softened, each stick cut into 8 pieces
Adjust oven rack to lower-middle position and heat oven to 350ºF. Generously grease two 9 x 1½ in cake pans with vegetable shortening and cover pan bottoms with rounds of parchment paper or wax paper. Grease parchment rounds, dust cake pans with flour and tap out excess. (For cupcakes, line 10 cupcake tins with paper liners.)
Beat eggs, milk, and vanilla with fork in small bowl; measure out 1 cup of this mixture and set aside. Combine the flour, sugar, baking powder and salt in bowl of standing mixer fitted wtih paddle attachment' mix on lowest speed to blend, about 30 seconds. With mixer still running at lowest speed, add butter one piece at a time; mix until butter and flour begin to clump together and look sandy and pebbly, with pieces about the size of peas, 30 to 40 seconds after all butter is added. Add reserved 1 cup of egg mixture and mix at lowest speed until incorporated, 5 to 10 seconds. Increase speed to medium-high and beat until light and fluffy, about 1 minute. Add remaining egg mixture (about ½ cup) in slow steady stream, about 30 seconds. Stop mixer and thoroughly scrape sides and bottom of bowl. Beat on medium-high until thoroughly combined and batter looks slightly curdled, about 15 seconds longer.
Divide batter equally between prepared cake pans (or fill cupcake tins ¾ full); spread to sides and smooth with rubber spatula. Bake until cake tops are light golden and skewer inserted in center comes out clean, 20 to 25 minutes (for cupcakes, 15-18 minutes.) Cool on rack 10 minutes. Run a knife around pan perimeter to loosen. Invert cake onto large plate, peel off parchment, and reinvert onto lightly greased rack. Cool completely before icing.