Combine water, yeast, and 1 teaspoon of sugar in a small bowl; stir to combine. Let stand in a warm place until small bubbles form on the surface, about 5 minutes.
Meanwhile, heat milk, 8 tablespoons (1 stick) butter, salt, and remaining 2 teaspoons of sugar in a small saucepan over very low heat. Cook, stirring constantly, until sugar has dissolved and butter has melted. Be sure not to let the mixture become hotter than 115°, or it will kill the yeast. Remove from heat, and pour into a large bowl; add the yeast mixture. Stir until combined. Add 6 cups flour, and stir until mixture forms a soft dough. It may be necessary to add the remaining 1/2 cup flour.
Transfer mixture to a lightly floured work surface, and knead until the dough is smooth, 5 to 8 minutes.
Lightly oil a large bowl, and place dough in bowl. Cover, and let rise in a warm place until doubled in size, 30 to 45 minutes. At this point, dough may be stored, tightly covered, in the refrigerator for up to 2 weeks. Allow dough to reach room temperature before proceeding with the recipe.
Punch dough down, and divide equally in half. Place on a clean work surface, and cover loosely with a kitchen towel or inverted bowl. Let rest for 5 to 10 minutes.
Preheat oven to 375°. Lightly butter a baking sheet; set aside. Melt remaining 3 tablespoons butter; set aside.
Working with one piece of dough at a time, roll out on a lightly floured work surface until 3/4 inch thick. Using a 2 1/2-inch biscuit cutter, cut out about 2 dozen rolls. Place rolls on prepared baking sheet, and let rise until rolls have doubled in size, 15 to 20 minutes. Brush tops lightly with melted butter. Repeat with remaining dough.
Bake until golden brown, 15 to 20 minutes. Serve immediately.