Preheat oven to 350°F.
Place grated zucchini on a kitchen towel and lightly pat to absorb some of the liquid.
Combine plant milk, flax, brown sugar, vanilla, and vegan butter (or canola oil) in a bowl and whisk until smooth.
Mix in the zucchini with a spoon.
Add the flour, baking powder, baking soda, salt, and cinnamon into the wet ingredient mixture and mix gently to combine. Do not over mix!
Spoon batter into 12 muffin baking cups, then place in the oven for 20-25 minutes.
To test doneness, place a wooden toothpick into the center of a muffin. If toothpick comes out dry, muffins are done!
Remove from oven and cool on rack or cutting board until ready to eat.