1. Preheat oven to 350*F (175*C). Grease and lightly flour a 13 x 9 x 2-inch baking pan (or, two 9 x 1 1/2-inch round pans, or three 8 x 1 1/2-inch round pans). Set aside.
2. In a large mixing bowl combine the flour, sugar, baking powder and salt, mixing well. Add the milk, shortening and vanilla and beat with an electric mixer on medium to medium-high speed for 2 minutes, scraping sides of bowl as needed. Add the eggs and continue beating an additional 2 minutes. Pour batter into prepared pan(s).
3. Bake the 13 x 9 x 2-inch cake for 40 to 45 minutes (or the 9-inch cakes for 30 to 35 minutes; the 8-inch cakes for 20 to 25 minutes), or until a wooden pick inserted near center of cake comes out clean, or until cake springs back when touched lightly in the center.
4. Cool the 13 x 9 x 2-inch cake on a wire rack. (Cool the 9 or 8-inch cakes on wire racks for 10 minutes; remove from pans and cool completely on wire racks.) Frost as desired.