In the bowl of a stand mixer, place the flour, xanthan gum, tapioca starch/flour, instant yeast, and granulated sugar, and whisk to combine well. Add the salt, and whisk again to combine.

Add the milk, melted butter, and egg whites. Using the paddle attachment, beat vigorously until the mixture comes together in a clump and clears the sides of the bowl. Keep beating until it begins to look whipped, and sticks to the side of the mixing bowl again (about 6 minutes total).

Transfer the mixture to a lightly oiled bucket or bowl with a very tight-fitting lid. Refrigerate the dough for at least 30 minutes and up to 3 days in the refrigerator.

Grease a quarter sheet pan or 2 8-inch round cake pans for baking. Flour a clean, dry work surface very lightly with tapioca starch. Divide the dough in half, then each half into 8 equal portions, for 16 pieces, each about 2 ½ ounces in weight.

Shape each piece of dough into a round and place in the baking pan(s) either touching or a bit more than 1-inch apart. Cover with lightly greased plastic wrap and let rise until about 150% of their original size.

Preheat your oven to 375°F. Once the rolls are properly risen, remove the plastic wrap and brush generously with melted butter.

Bake until an instant read thermometer inserted into the center of each roll reads about 190°F. If the rolls are touching, lower the oven temperature to about 350°F at 18 minutes and continue to bake for about another 5 minutes.

Remove the pan from the oven, and brush again with melted butter and serve warm.