1. Adjust oven rack to lower-middle position and heat oven to 350 degrees. Generously grease two 9-by-1 1/2-inch 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.
2. Beat eggs, milk, and vanilla with fork in small bowl; measure out 1 cup of this mixture and set aside. Combine flour, sugar, baking powder, and salt in bowl of standing mixer fitted with 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 (setting 6 on KitchenAid) and beat until light and fluffy, about 1 minute. Add remaining egg mixture (about 1/2 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. (To mix using hand mixer, whisk flour, sugar, baking powder, and salt in large bowl. Add butter pieces and cut into the flour mixture with a pastry blender. Add reserved 1 cup of egg mixture; beat with hand mixer at lowest speed until incorporated, 20 to 30 seconds. Increase speed to high, add remaining egg mixture, and beat until light and fluffy, about 1 minute. Stop mixer and thoroughly scrape sides and bottom of bowl. Beat at high speed 15 seconds longer.)
3. Divide batter equally between prepared cake pans; spread to sides of pan and smooth with rubber spatula. Bake until cake tops are light golden and skewer inserted in center comes out clean, 20 to 25 minutes. (Cakes may mound slightly but will level when cooled.) Cool on rack 10 minutes. Run a knife around pan perimeter to loosen. Invert cake onto large plate, peel off parchment, and re-invert onto lightly greased rack. Cool completely before icing.
Makes two 9-inch cake layers