Preheat oven to 350 degrees Fahrenheit. Lightly grease 12 donut molds or a muffin tin.
In a medium bowl, whisk together the whole wheat flour, all purpose flour, baking powder, salt, cinnamon, and nutmeg. Set aside.
In a separate large bowl, cream together butter and brown sugar on medium speed until light and fluffy. Add the eggs one at a time, and mix well after each addition until incorporated. Beat in the vanilla extract and scrape the bowl when necessary.
Add the flour mixture into the wet ingredients and mix on low speed until incorporated. Then add in the apple cider and applesauce while mixing on low speed. Scrape the bowl well to make sure all the ingredients are mixed together.
Spoon the batter into the donut or muffin tin and fill them around 2/3 of the way up. This can also be done with a piping bag. Bake for 12-15 minutes if making donuts or 15-20 minutes if making muffins or until a toothpick inserted comes out clean. (My muffins took around 18 minutes)
While the donuts bake, in a small bowl, whisk together the ¼ cup of sugar and teaspoon of cinnamon to make the cinnamon sugar topping. In a separate small bowl, melt the 2 tablespoons of butter.
When done baking, let the donuts cool in the tin for 5 minutes. After 5 minutes, remove the donuts from the tin and brush on the melted butter. Then immediately roll in the cinnamon sugar while still warm. Serve warm. If there are leftovers, store them in the fridge and reheat in the microwave or toaster oven when ready to serve.