Preheat oven to 350 degrees F. Coat a mini donut pan with baking spray.
In a medium bowl, whisk together the flour, baking powder, cinnamon, ginger, salt, nutmeg and cloves.
In a small bowl, whisk together the sugar, egg and vanilla extract. Add in the buttermilk and melted butter.
Pour the wet ingredients into the dry in one addition and mix to combine. Fold in the grated carrots and walnuts.
Transfer batter into a pastry bag (or ziplock bag) and fill the prepared donut pans. Fill each about 2/3 full. Bake donuts for 6-7 minutes or until a toothpick comes out clean. Let cool in pan for 1 minute before turning out onto a cooling rack.
To make frosting: whip cream cheese until smooth. Add powdered sugar and 2 tablespoon milk. Mix until combined. For a thinner consistency, keep adding milk, one tablespoon at a time, until frosting is pourable.
Ice cooled donuts with icing. Let icing set, about 20 minutes, before enjoying.
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