In a liquid measuring cup, combine the milk and apple cider vinegar. Stir to combine and let stand for 5-10 minutes or until the milk thickens to a consistency resembling buttermilk. Also, melt butter in the microwave and let stand to cool.
In one bowl, combine the wet ingredients: apple sauce, apple cider, eggs, granulated sugar, brown sugar, vanilla extract, milk/vinegar mix, and melted butter (once cooled). Mix with a hand whisk until combined.
In a seperate bowl, combine the dry ingredients: flour, baking powder, baking soda, salt, cinnamon, and apple pie spice. Whisk to combine.
Add the wet ingredients into the dry ingredients and fold into each other until combined.
Pour in the dehydrated apple bits and fold into the batter.
Scoop the batter into a piping bag, or a gallon sized ziplock bag. Cut the corner off of one end and pipe the batter into a greased donut pan.
Bake donuts at 375°F for 10-12 minutes or until the tops spring back when slightly pressed down Let cool completely before icing.