Preheat the oven to 350° Farenheight. Prepare a donut pan with non-stick cooking spray. Set aside.
In a medium bowl add the egg, brown sugar, almond milk, olive oil, and vanilla extract. Whisk together until completely combined.
In a large bowl whisk together the flour, cinnamon, baking powder, baking soda, ginger, salt, nutmeg, and clove.
Add the wet ingredients and whisk until fully combined.
Stir in the carrots and chopped pecans.
Fill each donut pan cavity with the donut batter 2/3 of the way.
Bake for 14-16 minutes. Allow them to cool completely before frosting.
Using an electric standing mixer with a paddle attachment combine the cream cheese and butter together on medium speed for 2 minutes.
Add in the vanilla extract, heavy cream, and salt. Mix until combined.
Add the powdered sugar 1/2 cup at a time until you reach your desired consistency.
Frost onto the cooled donuts.