Preheat oven to 375 degrees and prepare 12 piece muffin pan with muffin liners. If you don't have muffin liners, lightly coat with non-stick cooking spray or lightly grease with oil or butter.
Add the dry ingredients (flour, coconut sugar, baking soda, cinnamon, spices, salt) to a large mixing bowl and stir to combine.
2 cups whole wheat flour, 1/2 cup coconut sugar, 1 1/2 tsp baking soda, 2 tsp cinnamon, 1/2 tsp cardamom, 1/2 tsp ginger, 1/2 tsp nutmeg, 1/2 tsp salt
Add the grated carrot to the flour mixture and stir until the carrot is mixed in and coated with flour.
1 cup peeled and finely grated carrot
In a small bowl whisk together the wet ingredients (applesauce, coconut oil, dairy-free milk, vinegar). Be sure to use room temperature milk and applesauce so they don't cause the coconut oil to harden. You can warm them briefly in the microwave if they're cold.
2/3 cup unsweetened applesauce, 1/4 cup coconut oil, 2 tsp vanilla extract, 1/2 cup dairy-free milk, 1 tsp apple cider vinegar
Make a "well" in the centre of the dry ingredients and pour the wet ingredients into the whole. Fold together until all of the dry ingredients are mixed in and wetted.
Add the crushed walnuts and fold in a few times to mix throughout.
1/2 cup crushed walnuts
Using a large spoon or ice cream scoop, evenly distribute muffin mix into the prepared muffin tins. Place in the preheated oven and bake for 20 minutes, or until a toothpick can be inserted in the centre of the muffin comes out clean.
When ready remove from oven, lift out the pan and place on cooling rack for 10 minutes.