Preheat oven to 350 degrees
Line two cupcake/muffin tins with cupcake cups/liners (about 12 cupcake liners)
Whisk together the flour, baking powder, baking soda, salt, cinnamon and nutmeg.
Add in the applesauce, non-dairy milk, vanilla extract, sugar, coconut oil (or canola oil), carrots. Mix until just combined. Stir in walnuts and mix until evenly distributed.
I like to use a cookie scoop to scoop an even amount into the cupcake cups. You should fill it about 3/4 of the way.
Bake for about 30 minutes or until a toothpick comes out clean from the center.
Let them cool completely. In the meantime, prepare the frosting by placing vegan butter in a mixing bowl. Using preferably a stand mixer or electric hand mixer, beat the butter until creamy. Add in the vegan cream cheese and mix until creamy. Sift in the powdered sugar and stir until well combined.
Once the cupcakes are completely cooled, top with frosting and enjoy! I like to put them in the fridge for about 30 minutes before enjoying.