Preheat oven to 325 degrees. Spray a doughnut or muffin pan with nonstick cooking spray.
Whisk eggs together with apple butter, 1/2 cup sugar, buttermilk and brown sugar in a large bowl.
In a separate bowl, combine the flour, baking powder, baking soda and salt. Fold the flour mixture into the wet ingredients. Batter will be sticky. Fill a doughnut or muffin pan 2/3 of the way with the batter. Bake for 20 minutes.
In a shallow bowl, mix the cinnamon and 1 cup sugar together. Allow the doughnuts to cool, then dip into the cinnamon/sugar mixture.