Preheat the oven to 350 degrees F. Line a muffin pan with parchment paper liners. Place the grated carrots in a bowl with a little bit of water and microwave them for 30 seconds This will just soften the carrots up a bit - I think it makes for a nicer texture inside the muffins. Set the carrots aside to cool, then drain the water out.
Mix the melted buttery spread and sugar together. Add the grated carrot, vanilla, vinegar, and non-dairy milk and stir.
Add the flour, baking powder, salt, and cinnamon to the bowl and mix well.
Spoon the batter into the prepared muffin tin, filling each liner about ⅔ full. You will have some batter left over.
Bake at 350 degrees F for about 22-24 minutes, or until the muffins are golden brown.
Allow the muffins to cool in the pan for about 15 minutes, then move to a wire rack to finish cooling.
Repeat steps 4-6 with the remaining batter. This recipe makes 18 muffins.