Preheat the oven to 400°F. Coat the doughnut pans (you'll need two 6-cavity pans) with nonstick spray or oil, and sprinkle with sugar, shaking out the excess.
In a mixing bowl, whisk together the flour, baking powder, baking soda, salt and cinnamon; set aside.
In another bowl, whisk together the egg, brown sugar, apple butter, maple syrup, cider, yogurt and oil. Add the dry ingredients and stir just until moistened.
Divide half of the batter among the cavities in the prepared pans, spoon about 2 generous tablespoons of batter into each cavity. Don’t fill them to the top or your doughnuts will lose their holes when the batter puffs up while baking!
Bake 10 to 12 minutes, or until the tops spring back when touched lightly. Loosen the edges and turn the doughnuts out onto a rack to cool. If you only have one doughnut pan, you can clean the pan, re-coat it with oil and sugar, and repeat with the remaining batter.
ADD THE ICING:
In a medium bowl, whisk together the powdered sugar, cream cheese, and cinnamon, adding enough nonfat milk to create a spreading or dipping consistency. Dip the tops of the cooled doughnuts into the icing, then set right-side-up on a rack to let the icing set.
Notes
You will need a couple 6-cavity doughnut baking pans for this recipe.
You can also make these into 24 mini-sized doughnuts.