2 ¼cupflour(If you need it to be gluten-free, I have tested this with most brands of GF flour and they all worked well as long as they were grain-based mixes. I don't recommend grain-free mixes.)
1cuprolled oats
1 ½teaspoonbaking soda
1teaspoonsalt
1teaspooncinnamon
1teaspoonxanthan gum( If you are using gluten-free flour mix without it - Don't add if using regular flour.)
Mix 1/3 cup flax and 1/2 cup water together and set aside. (This is your egg replacer.)
Wash the zucchini, cut off the stem and hard spot on the end, then put into a food processor and chop until fine (or shred with a cheese grater if you don't have a food processor).
Wash and peel carrots then chop fine in a food processor or shred with a cheese grater.
Combine the 2 cups zucchini, 1 cup carrots in a bowl, and sprinkle with sugar (this will make the zucchini and carrots release some of their liquid.)
Add the flax mixture, 1/2 cup oil, 1/2 cup apple sauce, and 1 tbsp vanilla extract, and stir well.
Add the remaining dry ingredients (2 1/4 cup flour, 1 cup oats, 1 1/2 tsp baking soda, 1 tsp salt, 1 tsp cinnamon) and stir until all of the flour is incorporated.
(Sprinkle in 1/2 cup raisins, chocolate chips, or nuts if desired.)
Pour into oiled muffin tins and bake at 350°F (177°C) for 25 minutes until a toothpick inserted in the middle comes out clean.
Top with a small dollop of vegan buttercream or vegan cream cheese frosting if desired.
Notes
Little muffin tins are the perfect size for kids.
If using little muffin tins, reduce cooking time by 2-3 minutes.