- Grease 8½ by 4½-inch loaf pan with butter. Whisk 340 grams (1⅓ cups plus 2½ teaspoons) warm whole milk (105 degrees), 2½ teaspoons active dry yeast, and 4 grams (1 teaspoon) sugar together in bowl until dissolved. Let mixture sit until frothy and bubbly, 5 to 10 minutes.
- Meanwhile, combine 240 grams (2 cups plus 2 tablespoons) tapioca starch, 140 grams (1 cup) superfine sorghum flour, 70 grams (½ cup) millet flour, 2 teaspoons xanthan gum, 2 teaspoons baking powder, 1½ teaspoons table salt, and remaining 99 grams (½ cup) sugar in bowl of stand mixer.
- While whisking constantly, sprinkle 25 grams (2½ tablespoons) psyllium husk powder into yeast mixture. Set aside until thickened, about 1 minute, then add to dry ingredients along with 3 whole large eggs.
- Fit stand mixer with dough hook and mix on medium speed until flours are lightly hydrated, about 30 seconds. Increase speed to medium-high and knead until dough is thick and smooth, about 4 minutes.
- With mixer running, add 57 grams (4 tablespoons) softened unsalted butter (cut into 4 pieces), 1 piece at a time. Mix until butter is incorporated and dough is smooth and sticky, about 2 minutes.
- Dust counter lightly with tapioca starch. Transfer dough to counter and dust top with tapioca starch. Knead a few times to shape into ball, then into oval. Place dough inside prepared loaf pan and gently compress to fill pan. Cover with kitchen towel and let dough rise about 1 inch over rim of loaf pan, 45 minutes to 1 hour.
- Thirty minutes before dough is done rising, adjust oven rack to lower-middle position and heat oven to 375 degrees. When dough is ready, brush top with 1 beaten large egg. Bake until top is dark brown and bread has risen about 2 to 3 inches over rim of pan, about 40 minutes. Let bread cool in pan for 15 minutes, then gently remove from pan and place on rack to cool completely, at least 1 hour. Slice and serve.
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