Preheat the oven to 400°F.
Grease a donut pan and set aside.
In a large bowl, cream together the butter and sugar.
Next, mix in the applesauce, vanilla extract, salt, cinnamon, and pumpkin pie spice until well combined.
Add in the baking soda, baking powder, and apple cider vinegar. It will froth a bit, but stir until well combined.
Stir in the flour and apple cider until well combined.
Evenly distribute the batter into the greased donut pan and bake 10-12 minutes.
Let cool at least 10 minutes before transferring the donuts to a wire rack to finish cooling.
After at least 30 minutes the donuts can be topped with cinnamon sugar. In a small bowl whisk together the sugar and cinnamon until well combined. In another small bowl, melt the butter.
Dip each donut into the butter and then into the cinnamon sugar mixture. Let stand at least 5 minutes and enjoy!