Cream butter and sugar thoroughly with mixer. Add eggs and beat till mixture is smooth and silky, looking like mayonnaise and falls in ribbons from spoon. Beat in carrots.
Combine dry ingredients, sift and fold into carrot mixture by hand. Add vanilla. Spoon batter into 2 greased & floured 9" pans- no more than 3/4 full. Bake at 350 degrees for 30-35 minutes. Cool in pan for 5 minutes then remove to cake rack, carefully.
For frosting: Put butter and cream cheese in the bowl of a mixer. Process till mixture is smooth and free of lumps. Add confectioner, salt and vanilla. Mix till smooth. To achieve a stiffer consistency, if desired, add more confectioners' sugar or chill.