Brown the ground beef in a large pot or Dutch oven, breaking it into small pieces. Drain excess fat, transfer the beef to a bowl, and set it aside.

Melt 1 tablespoon of butter in the same pot. Add the onion, carrots, celery, basil, and parsley, then cook for 5–7 minutes, or until the vegetables begin to soften.

Add the chicken broth, cubed potatoes, and browned beef to the pot. Bring the soup to a boil, reduce the heat, cover, and simmer for 10–12 minutes, until the potatoes are tender.

In a separate saucepan, melt the remaining 2 tablespoons of butter. Whisk in the flour and cook for about 1 minute to make a smooth roux.

Gradually whisk the milk into the roux. Cook, stirring frequently, for approximately 3–5 minutes, until the mixture thickens and reaches a gentle boil.

Stir the thickened milk mixture into the soup. Add the salt and pepper, then simmer briefly until the soup is heated through.

Reduce the heat to low and stir in the cubed processed cheese gradually. Continue stirring until the cheese melts completely and the soup is smooth.

Remove the pot from the heat, or keep it on very low heat, and stir in the sour cream. Do not boil the soup after adding the sour cream.