Homemade Cheese Buns

Name: Homemade Cheese Buns
Prep time: 3 h
Cook time: 30 min
Total time: 3 h 30 min
Cuisine: American
Ingredients: 2 cups all purpose or bread flour ((add 1-2 tablespoons of flour if needed)); ¼ teaspoon salt; 1 teaspoon granulated sugar; 1 tablespoon olive oil; ½ cup freshly grated parmigiano (divided); 1½ teaspoons active dry yeast; ½ cup warm water* (not hot) divided ((add 1-2 tablespoons of flour if needed)); 1 large egg beaten; ½ cup grated mild Provolone cheese or Medium Cheddar Cheese; ¼-½ cup shredded Parmesan, Cheddar etc