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.