Preheat oven to 350℉. Spray a mini muffin tin with cooking spray and set aside.
In a small bowl, combine the flour, baking soda, baking powder, salt, and the spices. Stir with a spoon until fully incorporated.
In a large bowl, whisk together the egg, buttermilk, vanilla, applesauce, boiled cider, melted butter, and sugar until thoroughly combined.
Add the flour mixture to the wet ingredients, and stir together lightly just until combined. Scrape down the sides of the bowl with a rubber spatula and lightly fold any flour residue into the batter. Do not overmix.
Use a small cookie dough scoop to fill the wells of the prepared muffin pan. Bake the donut holes for 10-13 minutes or until a toothpick inserted into the center comes out clean. Remove from oven and let cool for 5 minutes before transferring to a wire rack. During the baking time, combine the cinnamon and sugar for the topping in a small bowl. Set aside with the melted butter for the topping.
While the muffins are still warm, dip the tops of each donut hole into the prepared melted butter. Then role the entire donut hole in the cinnamon-sugar mixture. Serve the donut holes immediately or let cool completely. These are best enjoyed the day they are made!