In a large saucepan, brown ground beef until no longer pink. Drain grease (if desired) and set meat aside.
In that same saucepan, melt 1 Tablespoon butter over medium heat. Add in onion, carrots, and celery. Sprinkle basil and parsley on top. Saute until vegetables are tender (about 8-10 minutes).
Add potatoes and broth, then add ground beef back to the saucepan; bring the mixture to a boil. Reduce heat; simmer, covered, until potatoes are tender (which will take about 10-12 minutes).
While the soup cooks, place remaining butter (3 Tablespoons) in a small skillet over medium heat on the stove top.
Add flour and whisk together until butter starts to cook and get bubbly. Add butter/flour mixture to the soup. Reduce heat on stove top to low and stir in cheese, milk, salt and pepper; stir until cheese is melted.
Remove soup from stove top and stir in sour cream. Top with additional fresh parsley if desired.
Notes
*Note: We have only made this recipe using Velveeta. Shredded cheddar cheese will work, but it might not be as creamy as when you use Velveeta.