In a small saucepan, bring the apple cider to a simmer and stir occasionally. Simmer the cider for about 20-25 minutes, or until it is reduced to ½ cup. Set aside to cool (about 15 minutes) or place in the refrigerator in a heatproof bowl to speed up the process.
Once cider is cooled, preheat oven to 350°F and spray a mini muffin pan with nonstick cooking spray (I like Pam for Baking). Set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt.
In a separate bowl, whisk together the melted butter, egg, milk, brown sugar, granulated sugar, vanilla, and apple cider vinegar.
Add the wet ingredients to the dry ingredients and gently fold with a spatula. Before all of the flour is combined, add in the cooled ½ cup of apple cider and fold to combine. Do not overmix.
Using a 1 tablespoon cookie scoop, scoop dough into the mini muffin pan. Only fill the wells of the muffin tin about half full so that these look more rounded and less like muffins. Bake for 8-10 minutes. Donuts are done when they spring back after being lightly touched. You can place any extra dough in the refrigerator while the donuts bake.
Remove donuts from oven and cool on a wire rack for 5 minutes. Transfer donuts to the wire rack to cool completely and then bake the rest of your dough.
While the donuts are cooling, make the cinnamon sugar by combining sugar and cinnamon in a shallow bowl. Stir to combine.
Dip cooled donuts in melted butter and then roll the coated donuts in the cinnamon sugar mixture. Enjoy!