Coat a 9 X 13 inch pan with cooking spray and line bottom of pan with wax paper. Coat wax paper with cooking spray; set aside.
Place butter, brown sugar and granulated sugar in a large bowl; beat with a mixer at medium speed 5 minutes or until well blended. Add eggs and egg whites, 1 at a time, beating well after each addition; until pale and fluffy. Beat in vanilla extract.
Lightly spoon flour into dry measuring cups, level with a knife. Combine flour, baking soda, cinnamon and salt, stirring with a whisk. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture; mix after each addition. Stir in carrot. Spoon batter into prepared pan. Sharply tap pan once on counter to remove air bubbles. Bake at 350 degrees for 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan. Carefully peel off wax paper; cool completely on wire rack.
To prepare frosting, place the cream cheese, butter, vanilla and salt in a large bowl; beat with a mixer at medium speed until smooth. Gradually add 2 cups powdered sugar, beating at low speed until smooth (do not overbeat). Stir in the remaining 3/4 cup powdered sugar. Cover and chill 30 minutes. Spread frosting over top of cake. Garnish with sprinkles. Store cake loosely covered in refrigerator.
