Preheat the oven to 350°F (180°C). Line a muffin tray with muffin liners.
Sift all purpose flour into a mixing bowl and add light brown sugar, baking soda, baking powder, salt, cinnamon, nutmeg and ground ginger. Mix together.
Prepare your flax eggs by mixing 2 tablespoons of ground flaxseeds with 6 tablespoons of hot water. Let it sit for a minute to become gloopy.
Add the flax eggs, grated carrot, canola oil, vanilla extract and apple cider vinegar. Mix into a thick batter. If you have any difficulty with the batter coming together then just step away from the bowl for a couple of minutes, which will give the carrots time to release more moisture into the bowl. When you come back you'll be able to mix it into a thick batter.
Add chopped walnuts and mix in.
Divide the batter evenly between the 12 muffin liners in the muffin tray.
Bake for 22-25 minutes. Check for doneness by inserting a toothpick into the center of one of the muffins. It should come out clean.
Transfer the muffins to a wire cooling rack to cool and then enjoy!