¼ cup warm water (115°)
2 packets active dry yeast
1 ½ cups warm whole milk (115°)
½ cup unsalted butter, melted
¼ cup sugar
2 ¼ tsp salt
2 large eggs
6 to 6 ½ cups AP flour
1 egg (for glazing)
Place water in small bowl; sprinkle with yeast, and let stand until foamy, about 5 minutes. In large bowl, mix together milk, butter, sugar, salt, and 2 eggs.
Using a wooden spoon, stir in 6 cups flour, 1 cup at a time, until you have a soft, shaggy dough (if necessary, add up to ½ cup more flour). Turn dough onto a floured surface; knead until smooth and elastic, 5-10 minutes. Lightly oil a large bowl; place dough in bowl, turning to coat. Cover bowl with plastic wrap; let stand in warm spot until doubled in size, about 1 ¼ hours.
Butter 2 9×13-inch baking pans. Divide dough in half. Roll each half into a 15-inch rope; cut each rope into 15 1-inch pieces. Shape each piece into a ball. Arrange dough balls in prepared pans. (To make ahead: wrap pans well, and freeze, up to 2 months.) Cover pans loosely with plastic wrap; let stand in warm spot until rolls have doubled in size, about 1 ¼ hours.
Preheat oven to 375°. In small bowl, beat remaining egg until blended; brush onto rolls. Bake until golden brown, about 20 minutes, rotating pans halfway through. Let rolls cool 15 minutes before serving.