In a medium bowl, combine all of the dry ingredients.
With a fork, beat in the egg and applesauce until well blended.

On a lightly floured surface, knead dough 10 times.
Roll out to 1/2" thick.
Cut with a donut cutter, well-floured.

In about 1-1/2" of oil or fat, heated to 370°, fry the rings, tuning occasionally until done.
Drain on a rack, NOT paper towels.
Frost with sugar glaze or dust with powdered sugar.

For the glaze, mix the sugar and water.

Drizzle glaze over cooled donuts.