In large bowl, beat shortening with electric mixer on medium speed 30 seconds. Gradually add granulated sugar, about 1/3 cup at a time, beating well after each addition and scraping bowl occasionally. Beat 2 minutes longer. Add egg whites, one at a time, beating well after each addition. Beat in vanilla. On low speed, alternately add flour mixture, about one-third at a time, and 1 1/4 cups milk, about half at a time, beating just until blended.