Heat oven to 350°F. Spray 12-cup fluted tube cake pan with cooking spray.
In large bowl, mix oats, applesauce, brown sugar, carrots, egg product and oil with spoon until well mixed. Stir in remaining cake ingredients just until moistened. Pour into pan.
Bake 50 to 55 minutes or until toothpick inserted in center comes out clean. Cool in pan 10 minutes. Remove from pan to wire rack. Cool completely, about 1 hour.
In small bowl, beat cream cheese and powdered sugar with electric mixer on medium speed until smooth. Beat in milk and vanilla until well mixed. Place cake on serving plate. Spoon frosting over cake.