In a medium-sized mixing bowl, cream together the butter, vegetable oil, granulated sugar, and brown sugar until smooth.
Add the egg, beating to combine.
Mix in the baking powder, baking soda, cinnamon, nutmeg, allspice, ginger, salt, and vanilla.
On low speed, mix the flour into the butter mixture alternately with the apple cider and milk, beginning and ending with the flour and making sure everything is thoroughly combined. (So start with ⅓ of the flour, then all of the cider, then another ⅓ of the flour, then all of the milk, and finally the rest of the flour.)
Spoon the batter into the donut cavities, filling ⅔ to ¾ full. It helps to put the batter in a large zip-top bag, cut a corner off the bottom of the bag, and pipe the batter into each donut cavity.
Bake the donuts for about 10-11 minutes, or until the edges are lightly browned.
Let the donuts cool in the pan for about 2 minutes, and then flip them out onto a wire rack. Bake the remaining donut batter (there is usually enough batter for 1-2 more donuts).
Allow the donuts to cool for about 10 minutes before coating in cinnamon-sugar.