In a small bowl, whisk the quinoa, flour, baking soda, cinnamon, and salt together. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the brown sugar. Add the applesauce, honey, and vanilla extract and mix until combined. Add the dry ingredients to the wet ingredients and mix on low speed to combine. Fold in the grated carrots.
Cover and chill cookie dough in the refrigerator for at least 1 hour.
Preheat oven to 350°F and line a baking sheet with parchment paper. Scoop the dough into balls and place on the baking sheet, about 2 inches apart. Bake for 16-18 minutes. The cookies may still seem soft and not done, but remove from oven and allow them to cool for 10 minutes.
Notes
While I have not tested it yet myself, if you're having trouble finding the quinoa flakes, you should be able to swap in gluten free rolled oats as a 1:1 substitute.