In a large bowl, whisk together the gluten free flour, tapioca starch, instant yeast, sugar, xanthan gum, and salt. Add the warm milk, eggs, melted butter, and apple cider vinegar. Mix with a spatula or wooden spoon until a thick, sticky dough forms.Cover the bowl and let the dough rise in a warm place for about 1 hour, until it has puffed up noticeably.
While the dough rises, prepare the filling. Stir together the melted butter and minced garlic in a small bowl. In a separate bowl, toss together the mozzarella, parmesan, and parsley.
Grease a 9-inch round cake pan or cast iron skillet. Using a spoon and wet hands, scoop out a golf ball-sized piece of dough. Dip the bottom of the dough ball into the garlic butter, then roll it lightly in the cheese mixture. Place it in the prepared pan.Repeat with the remaining dough, nestling the balls close together. Sprinkle any leftover cheese mixture over the top and drizzle with any remaining garlic butter.
Cover the pan loosely with a kitchen towel and let the rolls rise for 30 to 40 minutes, until they look puffy and are touching each other.
Preheat the oven to 375 degrees F. Bake the rolls for 22 to 28 minutes, until the tops are golden brown and the cheese is melted and bubbly.
While the rolls bake, stir together the melted butter, garlic, and parsley for the topping. As soon as the rolls come out of the oven, brush the garlic butter topping all over them. Let cool for 5 to 10 minutes in the pan, then serve warm so everyone can pull them apart.