Preheat oven to 350° F. Grease two doughnut pans (see note) and set aside.
In a small bowl, combine the dry ingredients (flour, baking powder, cinnamon, and salt). Set aside.
In a large bowl, whisk together vegetable oil, eggs, sugar, applesauce, boiled cider (see note), and vanilla until combined.
Add dry ingredients to the wet ingredients. Mix just until combined. Spoon or pipe the batter into the prepared pans (see note).
Bake 13-15 minutes, or until a toothpick inserted in the center of the doughnut comes out clean. (Mini doughnuts will bake in 8-10 minutes.)
Allow doughnuts to cool slightly. While they're cooling, combine sugar and cinnamon in a plastic or paper bag.
Once the doughnuts are cool enough to be handled and not fall apart, coat the doughnuts in the cinnamon-sugar coating by shaking the doughnuts (1-2 at at a time) in the bag. Place the coated doughnuts on a wire rack to cool completely.
For Glaze:
In a small bowl, combine all glaze ingredients. If you don't have boiled cider, you can add a smaller amount of apple cider or apple juice. Dip doughnuts in the glaze. Allow glaze to set before serving.Enjoy!
Notes
Note on boiled cider: I buy pre-bottled boiled cider from King Arthur Flour (link [here]). I enjoy the flavor and it's convenient to have on-hand. It also keeps in the refrigerator for a long time! If you prefer not to buy boiled cider, you could boil cider in a small saucepan down to a syrupy consistency.Note on doughnut pan: I have owned a few brands of doughnut pans, and I like my Norpro pan the best by far (link [here]). If you prefer to make mini doughnuts, you can find a mini doughnut pan [here]. See recipe instructions for the bake time for mini doughnuts. Recipe makes approximately 48 mini doughnuts.