Preheat oven to 375°.
Coat 2 (8-inch) round cake pans with cooking spray, and dust pans with 1 tablespoon flour.
Lightly spoon 2 1/4 cups flour into dry measuring cups; level with a knife. Combine 2 1/4 cups flour, baking powder, cinnamon, salt, baking soda, and nutmeg in a medium bowl. Combine granulated sugar and next 7 ingredients (granulated sugar through egg) in a large bowl; beat well at medium speed of a mixer. Add to flour mixture, stirring just until moist. Stir in carrot.
Pour cake batter into prepared pans. Sharply tap pans once on counter to remove air bubbles. Bake at 375° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Cool completely on wire racks.
Place 1 cake layer on a plate; spread with 2/3 cup Cream Cheese Frosting, and top with other cake layer. Spread remaining frosting over top and sides of cake. Sprinkle walnuts over top of cake. Store cake loosely covered in refrigerator.