Heat oven to 350°F. Grease bottoms and sides of 3 (8- or 9-inch) round pans with shortening; lightly flour.
In large bowl, beat all cake ingredients with electric mixer on low speed 30 seconds, scraping bowl constantly. Beat 2 minutes on medium speed, scraping bowl occasionally. Pour into pans.
Bake 25 to 35 minutes or until toothpick inserted in center comes out clean. Cool 10 minutes; remove from pans to cooling rack. Cool completely, about 1 hour.
In medium saucepan, mix 1/2 cup flour and 1 1/2 cups milk with whisk until smooth. Cook over medium heat until mixture is very thick, stirring constantly. Remove from heat; cool 10 minutes. In large bowl, beat 1 1/2 cups sugar and the butter with electric mixer on medium speed until light and fluffy. Gradually add flour mixture by tablespoonfuls; beat on high speed until smooth. Beat in vanilla. Fill and frost cake, using 1 cup frosting between layers. Store covered in refrigerator.