Preheat oven to 350 degrees. Lightly grease a mini muffin pan and set aside.
Cream together the butter and Sugar In The Raw until light and fluffy. Add the vanilla, egg, applesauce, and milk, and mix well until completely combined.
In a second bowl, mix together the flour, baking powder, baking soda, salt, cinnamon and nutmeg.
Add the dry ingredients to the wet ingredients and mix until combined.
Fill the mini muffin cups 2/3 full (do not overfill!) and bake for 12-14 minutes or until light golden brown and a toothpick inserted in the center comes out clean.
Place the donut puffs on a wire rack to cool.
Brush cooled donut puffs with melted butter, and roll in the cinnamon sugar mixture to coat.