Combine flour and next 5 ingredients. Combine brown sugar, oil, and 4 egg whites; beat well. Add flour mixture to brown sugar mixture alternately with milk, beginning and ending with flour mixture. Mix after each addition. Stir in reserved pineapple, carrot, and 2 teaspoons vanilla. Pour batter into a 13- x 9- x 2-inch pan coated with cooking spray. Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean. Let cool.
Beat 1 egg white and cream of tartar at high speed of an electric mixer until soft peaks form.
Combine 1/2 cup sugar and reserved 2 tablespoons juice in a saucepan. Bring to a boil; cook, without stirring, over medium heat 3 minutes or until candy thermometer registers 238°. Gradually pour sugar mixture in a thin stream over beaten egg whites while beating constantly at high speed. Continue to beat at high speed 7 minutes. Combine cheeses and remaining 1/2 teaspoon vanilla; beat at high speed until fluffy. Add one-third of egg white mixture; beat just until blended. Fold in remaining egg white mixture. Spread over cake.