Put carrot, celery, onion and garlic in a food processor and pulse until finely chopped; place in the slow cooker bowl. Add diced tomatoes, broth, tomato paste and sugar to slow cooker. Add 1/2 teaspoon Italian seasoning, 1/2 teaspoon salt and the red pepper flakes. Stir in beef and cook on HIGH for 5 hours or LOW for 6 hours.
Using a slotted spoon, remove beef chunks from slow cooker and set aside. When cool enough to handle, shred beef and stir back into slow cooker. Add remaining 1/2 teaspoon Italian seasoning and 1/4 teaspoon salt. Cook another 30 minutes.
Meanwhile, cook pasta according to package directions, about 12 minutes; serve with meat sauce. Sprinkle with Parmesan cheese, if desired.