Hearty Meat Sauce

Name: Hearty Meat Sauce
Ingredients: 2 tablespoons extra-virgin olive oil; 1/4 teaspoon crushed red pepper flakes; 1 small onion, chopped; 1 carrot, finely chopped; 3 cloves garlic, minced; 2 tablespoons tomato paste; Two 28-ounce cans whole peeled tomatoes, coarsely crushed; 1 1/2 teaspoons sugar; Kosher salt and freshly ground black pepper; 8 ounces ground beef; 1 teaspoon dried oregano; 1 teaspoon dried rosemary; 1 teaspoon dried thyme; 1/2 cup freshly grated Parmesan, plus more for serving; [For Serving:] Hot cooked pasta