Garlic Bread Rolls

Name: Garlic Bread Rolls
Ingredients: 1 cup whole milk (at room temperature); 1 egg (large beaten); 1 envelope active dry yeast; 4 cups all-purpose flour (plus 3 tablespoons, plus more for dusting); 1 tablespoon kosher salt (plus teaspoon); 1 tablespoon sugar (plus 2 teaspoons); 9 tablespoons unsalted butter (cubed and softened); 5 ½ sticks unsalted butter; ⅔ cup garlic (from 2 large heads finely chopped); 1 ½ cups Parmigiano-Reggiano (finely grated); 2 tablespoons kosher salt; 2 teaspoons pepper; ½ cup all-purpose flour (plus 2 tablespoons); ½ cup Parmigiano-Reggiano (plus 2 tablespoons finely grated); 1 teaspoon kosher salt; 5 tablespoons unsalted butter (melted)