Combine Dry Ingredients. Add gluten-free flour, sugar, yeast, salt, and baking powder to a stand mixer and gently pulse with the paddle attachment on low speed to combine. (Do not use a hand mixer, dough hook, or whisk attachment.)
Add Wet Ingredients. With the mixer on LOW speed, gradually add warm milk, warm water, melted butter, and eggs, one at at time.
Beat. Turn the mixer speed up to HIGH and mix the dough for 3 full minutes to allow the dough to fully blend. It will look VERY sticky and wet--more like thick, sticky cake batter than bread dough. This is normal!
Cover & Chill. Use an oiled spatula to scrape down the edges of the bowl and form the dough into a ball. (Make sure to also scrape the bottom of the bowl to check for any unmixed spots!) Cover the bowl with plastic wrap and chill 20 minutes to make the dough easier to handle.