1. In a large pot, brown the ground beef over medium heat. Drain and set aside.
2. In the same pot, sauté the onions, carrots, and celery until tender.
3. Add the potatoes and chicken broth. Bring to a boil, then reduce heat and simmer until potatoes are tender.
4. In a separate saucepan, melt the butter. Stir in the flour and cook for a minute. Gradually whisk in the milk and cook until thickened.
5. Add the milk mixture to the pot along with the cooked ground beef. Stir in the shredded cheese until melted and smooth. Season with salt and pepper to taste.