Preheat the oven to 400 degrees F and grease a standard donut pan with nonstick spray.
Add the egg, milk, butter, applesauce, vanilla, and maple syrup to a medium bowl. Stir well to combine. Stir in the rest of the ingredients and spoon into prepared donut pan, filling each full. (You'll use a heaping 1/4 cup batter in each.)
Bake for 14-16 minutes or until lightly golden brown around the edges and a cake tester inserted into the center comes out cleanly.
Let cool in pan for about 2 minutes, then turn out onto a wire rack to cool.
Optional Cinnamon-Sugar Topping: Add the cinnamon and sugar to a bowl and stir to combine. Brush the top of each donut with a little butter. Invert the donut and rub gently into the cinnamon sugar mixture to coat.
Serve warm or at room temperature.
Notes
These are best eaten on the day they are made, but can be stored in an airtight container for up to 3 days. Reheat briefly before serving after the first day if desired.
If you don't have a donut pan, you can bake these in a mini muffin tin, filling to the edge, and baking at the same temperature and timing.
Gluten-free: Use a 1:1 style GF flour blend.
Dairy-free: Use a neutral oil like canola and nondairy plain unsweetened milk.
Use smooth applesauce for a consistency close to cake donuts. (Chunky applesauce will have chunks of apples which the kids may or may not mind!)
To make the batter a little sweeter, add 1 tablespoon sugar.