Preheat oven to 400°F. Grease two donut pans (6 donuts per pan) with non-stick cooking spray or butter. Set aside.
Place the first 5 dry ingredients in a medium bowl and whisk together. Set aside.
In a large bowl, beat the butter an sugar with an electric mixer until light and fluffy. Add eggs, pumpkin and vanilla. Mix until combined. With mixer on low, alternate adding the dry ingredients and apple cider. Then turn mixer up to medium and beat for about 30 seconds.
Pour batter into large ziptop bag or pastry bag, seal and cut off one of the corners. Pipe the batter into the prepared pans. You should have enough dough for about 10 donuts. Bake for 16-20 minutes. (Check them at 16 minutes.) Let cool.
Meanwhile, melt butter in a medium bowl. Set aside. Mix sugar and cinnamon together in another medium bowl. Dip cooled donuts in the butter, then the sugar mixture. They're ready to eat. Store leftover donuts (if you have any) in an airtight container for 2 days at room temperature or up to a week in the refrigerator.
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Notes
If you don't want the donuts gluten free, substitute all purpose flour and omit the xanthan gum