Preheat the oven to 350°F. Line muffin pans with 24 cupcake liners.
Mix together oil, applesauce, sugar, salt and eggs. Mix well to fully combine, but it's not necessary to use a mixer.
Add in flour, baking soda, salt and spices. Mix until just combined, do not overmix.
Fold in carrots, as well as nuts, raisins or coconut if using. Mix until just combined. Scoop into prepared muffin pan.
Bake for 21 to 24 minutes, or until a toothpick inserted into the center of one of the middle cupcakes comes out clean.
Remove from oven and allow to cool in pan for approximately 10 minutes, then remove and allow to cool completely on a wire rack. Once fully cooled, top with cream cheese frosting.