HEAT oven to 350 degrees F. Spray muffin tin with no-stick cooking spray or use individual baking cups.
STIR together flour, baking soda, salt, cinnamon and nutmeg in small bowl. In large bowl, whisk together oil, peanut butter, brown sugar and eggs. Add carrots, walnuts and coconut, stirring until combined.
ADD flour mixture and mix until combined (batter will be stiff). Spoon into prepared muffin tins, filling them 2/3 full.
BAKE 25 to 30 minutes or until toothpick inserted into center comes out clean. Cool 5 to 10 minutes. Carefully place on cooling rack and cool completely.
BEAT together frosting ingredients until fluffy. Spread on cooled cupcakes.