Cook the beef: In a large skillet, heat the olive oil over medium heat. Add the ground beef and cook, breaking it up with a spoon, until browned and fully cooked (about 5-7 minutes). Drain any excess fat and transfer the beef to the slow cooker.
- Prepare the soup base: Add the chopped onion, minced garlic, diced potatoes, diced carrots, and beef broth to the slow cooker with the cooked beef.
- Season the soup: Stir in the basil, parsley, salt, pepper, and Worcestershire sauce (if using). Mix everything together and set the slow cooker to cook on low for 6-7 hours, or on high for 3-4 hours, until the potatoes and carrots are tender.
- Add the dairy and cheese: About 30 minutes before serving, stir in the evaporated milk (or regular milk) and sour cream. Then, add the shredded cheddar cheese and stir until melted and smooth. Taste the soup and adjust the seasoning if necessary.
- Serve: Once the cheese has melted and the soup is creamy, ladle it into bowls and garnish with fresh parsley or green onions if desired.