Preheat the oven to 350 F. Line muffin cups with paper cupcake liners.
2
Sift together the flours, baking soda, salt, cinnamon and nutmeg. In a large stand mixer with the paddle attachment, combine the brown sugar, oil and eggs until well combined. Add the carrots, applesauce and vanilla. Add the dry ingredients and mix until combined. Stir in 1/4 cup of the chopped walnuts.
3
place in muffin cups. Bake about 20 minutes.
4
beat together the cream cheese, confectioners'' sugar and lemon zest until smooth and creamy. Frost the cooled cupcakes.