Preheat the oven to 350 degrees Fahrenheit. Grease your donut pan with a nonstick spray. Peel and grate your carrots.
In a medium bowl whisk together your flour, baking soda, baking powder, cinnamon, ground ginger, ground nutmeg, ground cloves, and salt. Set aside.
In a large bowl, mix the egg and brown sugar with a hand mixer, until light brown. Then add your milk, coconut oil and vanilla extract and stir all to combine.
Grab the bowl of dry ingredients and add them to the large bowl with wet ingredients. Don’t overmix, just stir to combine.
After everything has been mixed, add your carrots and simply fold them in.
Put the batter in a ziplock bag, cut off a small corner, and pour the batter into your donut pan. Make sure to fill for about 2/3 per donut.
Bake your donuts for 14-16 minutes over 350 degrees Fahrenheit, or until cooked inside. Once done, take out of the oven and let cool off on cooling rack. Do not turn the oven off yet.
Toast your walnuts and pecans for 5-6 minutes in the oven. Once done, let cool off and turn the oven off.
Prepare your icing by combining your cream cheese and butter. Mix these with the hand mixer until smooth. Add your powdered sugar until all ingredients are combined well.
Add your milk very slowly, make sure to test your consistency throughout to make sure it isn’t too thick or too thin.
Dip each donut in the icing, twist and turn to make sure they are covered. I used a small spoon to add a thicker layer and just spread it out.
Chop your walnuts and pecans and add to your icing.