Combine first 5 ingredients in a bowl; make a well in center of mixture.
Combine brown sugar and next 5 ingredients, stirring well with a wire whisk. Add brown sugar mixture to dry ingredients, stirring just until dry ingredients are moistened. Stir in carrot, walnuts, and 3/4 teaspoon vanilla.
Spoon batter into 2 (4-inch) loafpans coated with cooking spray. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes. Remove from pans, and let cool completely on a wire rack.
Combine powdered sugar, cream cheese, and 1/4 teaspoon vanilla, stirring until smooth. Spread evenly over tops of loaves.