*Prick a medium potato with a fork. Microwave on 100 percent power until tender, about 5-7 minutes. Halve, then scoop the flesh into a bowl and discard skin. Mash the potato.
Lightly brush an 8-inch round cake pan with some of the melted butter; set aside.
In a stand mixer fitted with a paddle attachment, combine the flour, sugar, salt, xanthan gum, and instant yeast.
With the mixer running on low, add in the water, egg, apple cider vinegar, mashed potato, and remaining melted butter. Beat on medium for 3 minutes, scraping down the sides of the bowl.
Using a large ice cream scoop, scoop the dough and place in the middle of the pan. Place the other 8 scoops side by side all the way around the pan. Smooth out the tops of the rolls with wet fingers.
Cover the pan with plastic wrap and let rise in a warm place for about an hour.
Bake in a 400°F oven for 25-28 minutes or until the tops of the rolls are golden brown and the internal temperature reaches 200°F. Let cool slightly before serving.