Preheat oven to 350 degrees, and lightly spray some oil in a large donut baking pan. Set aside.
In a medium bowl, whisk together the sorghum or brown rice flour, ground flaxseed, baking powder, salt, cinnamon, and nutmeg. Set aside.
Peel and finely grate your carrot. In a large bowl, mix the rice milk, shredded carrot, brown sugar, oil, and vanilla together until mixed.
Pour the dry mixture into the wet ingredients and stir well. This will look a bit thin at first, allow the batter to rest about 3-5 minutes to thicken a bit, stir again, then pour into the prepared donut pan.
Fill each donut well in the pan to about 1/4-inch from top. You'll have a little bit of batter leftover from 6 large donuts, so you can pour this extra batter into a mini donut pan or a mini muffin pan.
Bake for 18-20 minutes, or until a cake tester or toothpick inserted in the thickest part of the donut comes out clean. While the donuts are baking you can prepare the dairy free cream cheese glaze (instructions below).
Let the donuts cool in the pan about 15 minutes before removing to a wire rack to cool some more. I use the flat part of an orange peeler tool to help remove donuts from the pan, it works great!
Once the donuts are completely cool, top with your cream cheese glaze and serve immediately. TIP: don't glaze the donuts until you're ready to serve them.
Cream cheese glaze:
In a medium bowl, beat the cream cheese with a hand beater until softened (make sure you don't skip this step or the glaze will be lumpy).
Beat in the powdered sugar and vanilla.
Add 1 Tablespoon of rice milk or oat milk at a time to the cream cheese/powdered sugar mixture until it reaches the consistency you want.
Drizzle on top of your Gluten Free Carrot Cake Donuts before serving!
While I didn't add ginger to this recipe, you can add ginger if you like to have ginger in your carrot cake! Just start with 1/8 to 1/4 teaspoon ground ginger and add more to taste as you like.