Cream the butter in a stand mixer, then add in sugar and brown sugar and mix on medium speed until light and fluffy.
Add applesauce and vanilla extract and continue mixing until incorporated.
In a large mixing bowl, stir together flour, baking powder, baking soda, cinnamon, ginger, nutmeg, salt, and cloves.
Add half of the dry mixture to the wet ingredients, mixing until incorporated. Then add half of the nondairy milk and the apple cider vinegar. Add remaining dry mixture, then remaining milk and mix until the batter is smooth.
Fold in shredded carrots, raisins, and walnuts until evenly incorporated.
Using a large cookie scoop, portion the batter into lined muffin tins, filling about ¾ of the way. Bake for 25 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.