Preheat oven to 325 degrees F and spray a donut pan with nonstick cooking spray.
Mix all dry donut ingredients in a bowl before adding the egg, apple sauce, and chilled coffee. Mix until smooth like cake batter.
Spoon donut mixture into donut pan, spreading evenly and wiping excess away from the edges.
Bake for 6-8 minutes or until a toothpick comes out clean.
While the donuts are in the oven, mix together icing ingredients and set aside.
After removing the donuts from the oven and cooling briefly (2-3 minutes), remove them and either dip them in the icing mixture face down or set them on a plate and spoon icing on top.
Finish by drizzling as much caramel syrup as you'd like and adding a few chocolate sprinkles if that's your thing. Enjoy!