Preheat oven to 350 degrees and spray donut tins (I have two tins that make 6 donuts each) with avocado oil spray.
In a large mixing bowl, stir together dry ingredients (cassava flour through coconut)
Make a well in the center of the bowl and add the remaining four ingredients (eggs through carrots). Use a whisk to combine the wet ingredients, then gently incorporate dry ingredients until just mixed.
Transfer the donut batter into a gallon size Ziploc bag. Snip the corner with scissors to make a piping bag, then pipe a thick ring of batter into each well of the donut pans. (Batter should be about the same level as the top of the pan)
Bake for 12-15 min or until a toothpick inserted into one of the donuts comes out clean.
Allow to cool for 10 min or so, then transfer to a wire rack to cool completely.
While the donuts are baking/cooling, combine icing ingredients in a mixing bowl and beat with an electric mixer until fluffy. Transfer to a Ziploc bag and snip the corner so a thin drizzle of icing can be piped across the top of each donut. For a thicker icing layer, use a knife or spatula to spread icing over the top of each donut.