Add apple cider to a small saucepan over medium-high heat. Simmer & reduce cider to ¾ cup (~30-35 min). Pour into a medium mixing bowl & let cool completely.
Whisk the melted butter, buttermilk & eggs into the cooled cider.
In a large mixing bowl, whisk together flour, brown sugar, ½ cup of granulated sugar, 1 tbsp of cinnamon, baking powder, salt, baking soda & nutmeg until combined.
Add wet ingredients into dry, mixing on low speed until a slightly tacky dough forms, adding additional flour if needed. Cover with plastic wrap & chill until the dough is firm, at least 1 hour & up to 12 hours.
Fill a Dutch oven with 3” of oil. Heat the oil to 350ºF, letting the oil come back to heat between batches. Turn the chilled dough out onto a generously floured, clean work surface. Flour the top of the dough (it'll be sticky) & pat the dough into a ½“ thick rectangle.
Dip a 3” round cookie cutter or biscuit cutter in flour & stamp out donuts. Use a 1” cutter to cut the holes in the center. (Save the cutouts to make donut holes). Add each donut to individually cut squares of parchment paper.
Working a few at a time, add donuts with parchment paper to hot oil, removing paper with tongs as soon as it separates from donut. Fry until golden brown on both sides, flipping halfway through (~3 min for large donuts & ~2 min for holes).
Use tongs or a slotted spoon to transfer to a wire cooling rack for about 5 minutes.
In a shallow bowl, stir together the remaining granulated sugar & the remaining cinnamon. Toss the donuts in the cinnamon sugar & serve.