Preheat oven to 350°F.
Line a 12-cup muffin tin with foil liners or gently spray it with cooking spary.
In a medium bowl, whisk together the flour, oats, sugar, baking powder, baking sodea, cinnamon, nutmeg, ginger, and salt.
In a large bowl, whisk together the non-dairy milk, applesauce, vinegar, and vanilla.
Whisk the dry ingredients into the wet ingredients until just combined and there is no visible white flour.
Stir in the shredded carrots until evenly distributed throughout.
Pour batter into the muffin tin until each cavity is about ¾th full.
Bake for 22 to 25 minutes, until a toothpick comes out clean.