Grease a doughnut pan (metal or silicone), with a light and even coating of butter and a dusting of flour, shaking off any excess flour. Set aside.
Begin by reducing the apple cider. This step is important because without a concentrated and thickened cider, the pronounced apple flavor is lost. To reduce, add the apple cider to a medium saucepan over low heat and simmer, stirring occasionally, until the cider reduces to 1/2 cup (118 ml), about 20-25 minutes. Set the cider aside to cool for 15 minutes.
In the meantime, preheat the oven to 350 F. (177 C.).
In a large mixing bowl, add the flour, baking powder, apple pie spice, and salt, mix together and set aside.
Using a stand mixer, add 10 tablespoons butter, brown sugar and only 1/4 cup (59 g) of sugar and mix to cream the ingredients together, about 3 minutes or until light and fluffy, scraping the bowl as needed. Add the eggs, one at a time, until well incorporated, scraping down the sides as needed. Add the vanilla and mix again to incorporate.
Add the flour mixture and mix on low speed until well incorporated. With the mixer still running on low speed, add the apple cider in slowly. Mix to incorporate, scraping the sides again as needed.
Fill a large piping bag or plastic zip-top bag with the batter and snip off the corner end. Alternatively, you can use a spoon, though it’s a little messier. Pipe the batter into the pan, filling just about halfway.
Bake until lightly brown, about 15-20 minutes for large doughnuts, and 10 minutes for the mini, don’t overcook. To test if it’s done, use a toothpick to insert into one of the doughnuts, if it comes out clean, they’re done. Allow the doughnuts to cool for a few minutes before transferring to a wire rack. Continue the same baking process with the leftover mixture.
In the meantime, prepare the cinnamon topping. Combine 1 cup of granulated sugar and 2 teaspoons of ground cinnamon in a medium bowl, adding more if desired to suit your preferences. Mix well to incorporate and set aside.
Melt 6 tablespoons (84 g) of butter. Take the cooled doughnuts and dip both sides into the melted butter, allowing any excess to drip off. Lightly dip each side of the doughnut into the cinnamon and sugar topping, shaking off any excess. Allow to dry on a cooling rack or serve right away.
Notes
Leftover doughnuts will keep well if stored in an airtight container for up to 2 days.