Place olive oil, onion, garlic, celery, and carrots into a pot or dutch oven on medium heat until caramelized, around 2-3 minutes.
Pour 1 cup of beef broth, bring to simmer, scraping the bottom of the pot or dutch oven to dissolve brown bits into the liquid.
Add thawed shredded beef to the pot.
Add crushed tomatoes, tomato paste, remaining beef broth, dried thyme, bay leaves, and sugar into the pot.
Simmer on low heat for 1-2 hours covered or until vegetables are tender.
Remove bay leaves before serving.
Add salt and pepper to taste.
Serve with favorite cooked pasta and add parmesan cheese as garnish, if desired.
