Brown ground beef, onion, and celery in a large saucepan or stockpot; add a little olive oil if necessary.
Add the diced red bell pepper and cook for 1 minute longer. Add the chicken broth, carrots, potatoes, parsley, and basil. Bring to a boil. Reduce heat to low; cover and simmer for 30 minutes, or until vegetables are tender.
In a saucepan, melt butter over medium low heat; stir in flour until smooth, about 30 seconds. Slowly stir in the half-and-half or milk. Stir in cheese. Continue cooking, stirring, until cheese is melted and the mixture is thick and begins to bubble. Stir the milk mixture into the soup mixture until well blended. Taste and add salt and pepper as needed. Heat thoroughly.