First, preheat your oven to 350 degrees Fahrenheit. Then, take your butter, apple cider, sour cream, and egg out of the fridge, if you haven't already, so that they are all at least room temperature.
Next, mix together the nutmeg, cinnamon, salt, flour, and baking powder in a bowl and set aside.
And then, whisk the sourdough discard, apple cider, sour cream, vanilla extract and the egg together. It's alright if this mixture looks a little clumpy. Be sure not to overmix!
Then, melt the butter and mix the cane sugar and brown sugar into the butter. Now add the sourdough discard mixture to the nutmeg mixture and mix everything together. Next, add the butter mixture to the batter. Again, make sure that you don't overmix!
Now, grease the donut pan. Add the batter to a Ziplock bag and cut a small corner off of one of the sides. Squeeze the batter into each donut cavity so that the cavities are 1/2 to 3/4 full. Then, put the donuts into the oven for about 12 minutes. You can tell that the donuts are done baking when they feel springy/ spongy to the touch.
While the donuts are cooking, melt the 6 tablespoons of butter. Then add sugar and cinnamon to a separate bowl.
After, the donuts are done baking, pull them out of the oven and let them cool down for a few minutes before removing them from the donut pan.
Next, using tongs, or even your hands, dip the donuts into the butter. Additionally, you could just do one side of the donut, that's what I did, or both sides. Then, take the donut and dip it into the sugar/cinnamon mixture.
Finally, enjoy your freshly baked sourdough apple cider donuts!