In the mixing bowl of your electric mixer, mix together flour, xanthan gum, instant yeast, sugar, and salt.
With mixer running on low speed, add in the water, melted butter (or substitute), egg, and cider vinegar.
Mix on medium speed 3 minutes.
Spray 8" or 9" round cake pan or pie plate with cooking spray. Using a 2" scoop or 1/3 cup measuring cup, scoop dough into 9 mounds in the pan. I place one mound in middle, then scoop 8 mounds of dough side by side all the way around the pan.
Dip your fingertips into warm water and use to smooth out the tops of the rolls, continuing to wet fingers as needed.
Cover with a dry towel and let rise in a warm place 45 minutes to 1 hour.
During the last few minutes that the rolls are rising, preheat oven to 400°.
Bake in 400° oven for 26-28 minutes. Tops should be golden brown and if you measure temperature of dough, it should measure 200°.
Brush rolls with additional 1/2-1 Tablespoon of melted butter.
Please see blog post for information on egg-free and dairy-free substitutions. If you would like to use a different flour blend, please read through the reader comments below to see what flour blends have worked well for other readers! Make sure you measure the flour by weight!