Preheat oven to 400 degrees F. Lightly coat 12-24 cups of a mini muffin pan with cooking spray.
In a large mixing bowl, combine flour, baking powder, baking soda, salt, and cinnamon. In another large bowl, whisk together egg, brown sugar, apple butter, vanilla extract, honey, apple cider, yogurt, and oil. Whisk wet ingredients into dry ingredients until just mixed; do not overmix.
Using a tablespoon or cookie scoop, fill muffin cups 3/4 full. Bake for approximately 10-12 minutes.
While baking, melt butter in a microwave safe dish. Combine cinnamon and sugar in another dish. Roll warm donut holes in melted butter, gently shake off excess, and roll in cinnamon-sugar mixture.