Spaghetti Burgers

Name: Spaghetti Burgers
Ingredients: Vegetable oil, for frying and brushing; Kosher salt; 4 ounces spaghetti; 1/4 cup grated parmesan cheese; 1/2 small onion, cut into chunks; 5 cloves garlic, smashed; 1/2 cup fresh basil, plus 2 tablespoons thinly sliced, for topping; 1/4 cup fresh parsley; 1 1/4 pounds ground beef chuck; 3/4 cup grated parmesan cheese; 1 cup tomato sauce, plus 1 cup warmed for dipping; 1 teaspoon dried oregano; Kosher salt and freshly ground pepper; 4 slices mozzarella cheese; 4 hamburger buns, split; 1 tablespoon extra-virgin olive oil