In the bowl of a stand mixer (See Recipe Notes), 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. The mixture will come together in a clump and clear 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. The container should be large enough for the dough to nearly double (although it won’t double fully).
Chill the dough
Refrigerate the dough for at least 30 minutes and up to 3 days in the refrigerator. Do not let the dough rest/rise for too long, or your rolls will rise much more irregularly after shaping.
If your dough has been refrigerated for more than 1 hour, allow it to sit at room temperature until no longer very cold to the touch before working with it.
Shape the rolls
Grease a quarter sheet pan or 2 8-inch round cake pans for baking, and set them aside. You will later decide if you’d like to crowd the rolls, and have them rise then bake touching, or have them separate.
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 1/2 ounces in weight.
Working with one piece of dough at a time, cup your fingers around the dough, keep the side of your palm on the surface, and move your hand in tight circles to coax the dough into a round.
Place the shaped rounds of dough in your chosen baking pan(s) either touching (they will rise mostly up), or a bit more than 1-inch apart, taking care not to crowd them (the will rise up and out).
Let rise
Cover the pan(s) with lightly greased plastic wrap, place in a warm, draft-free location, and allow to rise until about 150% of their original size (they won't quite double).
This rise can take anywhere from 45 minutes to hours, depending upon the ambient temperature in your kitchen. Overproofing is not very likely, and can be detected when the surface of the rolls begins to look pockmarked.
When the rolls are nearing the end of their rise, preheat your oven to 375°F. Once the rolls are properly risen, remove the plastic wrap from the pan(s), and brush generously on all exposed sides with melted butter.
Bake
Bake until an instant read thermometer inserted into the center of each roll reads about 190°F.
If there is any space between the rolls after they’ve risen, they will take around 20 minutes until fully baked.
If the rolls are touching one another, lower the oven temperature to about 350°F at 18 minutes and continue to bake for about another 5 minutes or until the center reaches 190°F.
Remove the pan from the oven, and with the rolls still in the hot pan, brush again with melted butter and serve warm.
Video
Notes
Flour blends: I recommend Better Batter’s original blend or my Nicole’s Best multipurpose blend (with 3 teaspoons added xanthan gum). King Arthur's gluten free bread flour can work but makes denser rolls, so consider adding 2 tablespoons more milk. Avoid Cup4Cup and Measure for Measure here—they won't produce the right texture.Bob’s Red Mill 1-to-1 isn't ideal, but in a pinch, it can work if you add 1½ teaspoons extra xanthan gum.To make your own blend using one of my “mock” recipes, please see the all purpose gluten free flour blends page.Using active dry yeast: You can swap instant yeast for active dry yeast—just use 15 grams instead of 12 and proof it in some of the warm milk before adding.No stand mixer? A food processor with the plastic blade works in a pinch. Don’t use a hand mixer or mix by hand; the dough needs vigorous mixing to whip up properly and create a smooth shaped roll.