Scrub the carrots clean, trim the end and peel the skin off. Cut them into smaller pieces and shred them in a food processor or shred them with a box grater. This should yield 1 ¼ cups.

Preheat the oven to 350°F.

Line a regular size muffin pan with cupcake liners and set aside.

Add buttermilk, oil, egg and vanilla extract to a large mixing bowl and beat until smooth. Add brown sugar and mix until the sugar is completely dissolved. Add shredded carrot and mix until evenly distributed.

Sift together flour, baking soda, baking powder, cinnamon and nutmeg into a medium mixing bowl. Add the salt and mix thoroughly with a whisk. Add the flour mixture to the liquid mixture and fold until incorporated. Fold in the chopped walnuts.

Divide batter evenly among twelve cupcake cavities using a large ice cream scoop and bake for 17 - 19 minutes until a toothpick inserted in the middle of the cake comes out clean with just a few crumbs attached.

Remove from the oven and let cool on a wire rack for 10 - 15 minutes. Remove cupcakes from the pan, and allow to cool completely on a wire rack.

Add vanilla extract and beat to combine.

Add powdered sugar and stir until incorporated, gradually increase the mixer speed and beat until fluffy.

Add a scoop of frosting on each cupcake and spread it with an offset spatula or butter knife. Add chopped walnuts on top if desired. Serve right away or refrigerate until ready to serve.