Heat 1 tbsp olive oil in a large pot over medium high heat. Saute carrot, celery, green bell pepper, onion, mushrooms and garlic until softened, about 3 minutes. Remove from pot and set aside.
Season cubed short ribs with salt and pepper. Add remaining 1 tbsp olive oil to pot and working in batches, brown cubes of short ribs over medium high heat. When batch is browned, remove to a bowl and continue to brown remaining.
Add red wine and beef broth, scraping up browned bits from bottom of pot. Add browned short rib cubes back to pot together with Prego, sugar, black pepper, fresh basil and red pepper flakes. Simmer on medium low for about 2 hours or until short ribs are fork tender.
Serve with large elbow macaroni that is cooked according to package directions. Garnish with freshly grated Parmesan cheese.