Preheat oven to 350°F (175°C) and grease a donut pan with baking spray.
Mix dry ingredients: In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.
Beat sugars and eggs: In a large bowl, beat granulated sugar, brown sugar, and eggs until light and fluffy.
Add wet ingredients: Mix in applesauce, yogurt, milk, melted butter, and vanilla until smooth.
Combine: Gradually add the dry ingredients into the wet mixture, stirring until just combined (do not overmix).
Fill pan: Spoon or pipe the batter into the donut pan, filling each cavity about ¾ full. Bake: Bake for 14–16 minutes, or until a toothpick inserted in the center comes out clean.
Cool: Let donuts cool in the pan for 5 minutes, then transfer to a wire rack.
Coat: In a shallow bowl, mix cinnamon and sugar. Brush each warm donut with melted butter, then toss in the cinnamon sugar mixture until coated.