Preheat oven to 350°F. Grease a 6-cavity donut pan with cooking spray.

In a large bowl, whisk together flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a separate bowl, whisk together applesauce, milk, egg, oil, and vanilla until smooth.

Pour the wet ingredients into the dry and stir until just combined. Do not overmix.

Pipe or spoon batter into the donut pan, filling each cavity about ⅔ full.

Bake for 12-15 minutes until donuts spring back when lightly pressed. Let cool in pan for 5 minutes, then remove.

Mix sugar and cinnamon in a shallow bowl. Place melted butter in another shallow bowl.

While donuts are still warm, brush each one with melted butter, then roll in the cinnamon sugar mixture until fully coated.

Repeat with remaining batter for a second batch. Serve warm.