Savory Dinner Rolls

Name: Savory Dinner Rolls
Ingredients: For the dough:; 1 1/2 teaspoons dry active yeast; 1/4 cup warm water; 3/4 cup warm milk; 2 tablespoons sugar; 1 teaspoon salt; 1 large egg; 4 tablespoons (1/2 stick) very soft, unsalted butter; 3 1/2 to 4 cups all-purpose flour; For the garlic-herb butter:; 4 tablespoons unsalted butter, at room temperature (1/2 stick); 1 small clove of garlic, peeled and minced, crushed to a paste with a little coarse salt; 1 teaspoon fresh rosemary leaves, finely minced; 1 teaspoon fresh thyme leaves, finely minced; 1 pinch kosher salt; 1 cup coarsely grated sharp cheddar cheese, or to taste