Preheat the oven to 375. Spray a muffin tin with cooking spray. Line it with muffin holders and set aside.
In a small jar combine the soy milk and rolled oats. Set aside for 10 minutes to allow the oats to soften. Note: Don't skip this step. Soaking the oats is important if you want fluffy muffins.
While oats soak, make the flax eggs. Ground 2 tablespoons of flaxseeds to a fine powder. Add 6 tablespoons of water and whisk together. Set aside until the mixture is thick and gelatinous; it should be the consistency of whipped eggs.
Mix together the flour, baking powder, baking soda, salt, and spices. In a separate bowl, combine the wet ingredients, including the carrots, mashed banana, soaked oats, and flax eggs. Add the wet ingredients to the dry and mix in until the flour is evenly hydrated and the batter is uniform. Fold in walnuts.
Scoop your batter into a greased muffin tin. Fill each muffin mold about ¾ of the way full and bake for 20-22 minutes, until a toothpick inserted in the middle comes out clean.
Remove the muffins from the oven and let them cool in the muffin tin for 10 minutes before flipping out to a wire cooling rack to cool completely.