In a 12 inch frying pan, thoroughly cook ground beef. Drain fat and set aside for now.
In a large 5-Quart pot with 1 tablespoon of the butter over medium-high heat, sauté onion, carrots, and diced celery with Italian seasoning, oregano, salt and pepper until onions have softened, 2 to 3 minutes.
Add in beef, potatoes, and chicken broth to the pot. Reduce heat to low, cover with lid, and simmer for 10 to 12 minutes, until potatoes are tender.
In a separate small frying pan, melt the remaining 3 tablespoons of butter over medium high heat and stir in flour until it starts to bubble, 2 minutes. Then add this mixture to the soup stirring well to mix.
Stir in cheese until fully melted.
Add in milk and bring back to a simmer. Then stir in sour cream until well mixed.
Remove from heat and serve hot.