Preheat oven to 350°F/177°C. Place liners in a muffin pan.
Sift together dry ingredients, flour, baking powder, baking soda, spices and salt.
In another bowl, beat together sugars and oil. Add in the eggs one at a time and then the vanilla extract.
Add the sifted dry ingredients in two batches. Fold in grated carrots and walnuts.
Scoop cupcake batter in the prepared cupcake pan. Bake for 18-20 minutes or until cooked. Set aside to cool.
Using a whisk attachment, whip cream cheese and butter until smooth. While the mixer is running pour the whipped cream. Add in the confectioner’s sugar and vanilla extract. Pipe frosting on cupcakes.