Shred your rainbow carrots. I like to use the shredding attachment on my food processor for this, but you can also do it by hand. Set the shredded carrots aside.
Combine the melted coconut oil, eggs, and vanilla extract in a bowl and whisk to combine.
Add the baking powder, coconut flour, and sugar to the coconut oil mixture and whisk again.
Add in your shredded carrots and mix until combined.
Spread the mixture in a greased 9x9 square baking pan. Bake 40-45 minutes until the sides are bubble, the carrots have started to brown and the center is set.
Remove the pan from the oven and let it sit for 10-15 minutes before cutting into it.
Notes
The nutrition facts presented here are estimates only and reflect 1/4 cup sugar used. The brands you use and product types chosen can change the nutritional information presented. To obtain the most accurate nutritional information, you should calculate the nutritional information with the actual ingredients you use.