Preheat oven to 400º.
Prepare donut tins by spraying well with cooking spray.
Set aside.
In a large mixing bowl, combine flour, sugars, baking powder, soda, salt, cinnamon, nutmeg and allspice.
Stir well and set aside.
In a separate microwaveable bowl, melt butter.
Add applesauce, buttermilk, vanilla and diced apple.
Whisk well to combine.
Add wet mixture to dry mixture and stir just until moistened.
Transfer ingredients to a zip lock bag (without the “stand and fill” bottom).
Cut off a corner and pipe the donut dough into the donut tins a little over ¾ full.
Bake in preheated oven for about 9-10 minutes or until donuts test done with a toothpick.
Remove from oven and cool for 10 minutes.
Dip top of donuts in butter.
Swirl in cinnamon-sugar mixture.
Turn donut over and coat the bottom with butter.
Place donuts right-side-up in cinnamon-sugar mixture and swirl lightly in mixture.
Sprinkle cinnamon-sugar mixture over top of the top part of the donuts. (I just used my fingers to do this).
Turn donut over.
Sprinkle the bottom of the donut with more cinnamon-sugar.
Do this a total of four times (for the top and four times for the bottom), until the mixture adheres well and the donuts are really well covered with the cinnamon-sugar mixture.
Place on wire racks to cool completely.