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Preheat oven to 350°F/177°C. Place liners in a muffin pan.
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Sift together dry ingredients, flour, baking powder, baking soda, spices and salt.
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In another bowl, beat together sugars and oil. Add in the eggs one at a time and then the vanilla extract.
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Add the sifted dry ingredients in two batches. Fold in grated carrots and walnuts.
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Scoop cupcake batter in the prepared cupcake pan. Bake for 18-20 minutes or until cooked. Set aside to cool.
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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.