Pre-heat oven to 350°F. Lightly oil a 12 cup muffin tin.
To make the flax egg, mix the ground flax seed with water in a small bowl. Let sit for 5 minutes. Mix together carrots, applesauce, coconut oil, lemon juice, maple syrup and vanilla extract in a medium sized bowl. Fold flax egg into wet mixture.
Whisk together the almond flour, oat flour, baking soda, salt, cinnamon and pumpkin spice in a large bowl.
Fold wet mixture into the dry mixture until completely combined with least possible stokes. Add in chopped walnuts and shredded coconut if using.
Fill muffin cups to the top. Bake for 25-30 mintues, or until tops are just browned. Let cool 10 mintues in pan. Enjoy!