Preheat oven to 350°F (175°C). Spray donut pan(s) with cooking spray.

In a mixing bowl, whisk together the egg, milk, applesauce, sugar, and vanilla until well combined.

Add flour, baking powder, cinnamon, and salt to the wet ingredients. Whisk until the batter is smooth.

Spoon the batter into the prepared donut pan, filling each opening almost to the top. Bake for 12-15 minutes or until a toothpick comes out clean.

Allow donuts to cool in the pan for a few minutes, then transfer to a baking sheet lined with parchment paper.

In a separate bowl, whisk together powdered sugar, cinnamon, applesauce, and water until smooth. Add water as needed to achieve a thick glaze.

Dip the top of each donut into the glaze, twisting gently to coat. Let excess glaze drip off and place the donuts glaze-side up on the lined baking sheet.

Allow donuts to rest for about 15 minutes to let the glaze set before serving.