Preheat oven to 350 degrees. Line 12 muffin cups with paper liners.
Sift together the flours, baking soda, salt, cinnamon and nutmeg.
In a large bowl, combine the brown sugar, oil and eggs with the electric mixer until well combined. Add carrots, applesauce and vanilla. Add the dry ingredients and mix until combined. Stir in 1⁄4 cup of chopped walnuts.
Divide the batter among the muffin cups. Bake about 20 minutes (until toothpick comes out clean).
While the cupcakes are baking, beat the cream cheese, sugar and lemon zest with an electric mixer to make the frosting.
Let the cupcakes cool completely. Frost cooled cupcakes and top them with the remaining two tablespoons of chopped walnuts.