Heat the olive oil in a large skillet over medium-high heat. Add the beef chunks and brown them on all sides for about 5 minutes. Transfer the beef to the slow cooker.
Add the chopped onion, minced garlic, sliced carrots, and sliced celery to the slow cooker.
Pour in the crushed tomatoes and beef broth. Stir in the tomato paste, dried oregano, dried basil, dried rosemary, salt, and black pepper until everything is combined.
Cover the slow cooker and cook on low for 8 hours or on high for 4 to 5 hours, until the beef is tender and the vegetables are soft.
Taste and adjust salt or pepper if needed. Ladle into bowls and top with chopped fresh basil before serving.