Cook the ground beef in a 3 quart saucepan. Drain off the fat and set aside.
In the same pan, add 1 tbsp butter and chopped onion, shredded carrots, parsley, basil, and celery. Saute until tender, about 5 minutes.
Add the broth, potatoes, and cooked ground beef and bring mixture to a boil. Reduce heat and simmer covered for 10-12 minutes or until the potatoes and tender.
In a small skillet, melt remaining 3 tbsp butter, and add the flour. Stir and cook for 3-5 minutes until bubbly. Add to the soup and bring to a boil. Stir and cook for 2 minutes. Reduce the heat to low.
Stir in the cheese, milk, salt and pepper. Cook and stir until the cheese is melted. Remove from heat and serve immediately.