Cook the beef in a large soup pot over medium heat until no longer pink. Drain off extra fat. Keep the beef in the pot.
Add the bell pepper and onion to the pot. Cook until the vegetables are just softened, approximately 5 minutes.
Add the cornstarch (if using), milk, beef stock, salt, and pepper. Stir. Bring to a boil over high heat.
Reduce heat to medium low and simmer for 10 minutes.
Remove from the heat. Add the cheese and stir until the cheese is melted.
Season to taste with salt and pepper. If too thick, add more milk or stock. If too thin, continue cooking down or add more cheese or cornstarch.
Notes
The cornstarch helps to thicken the soup, but the cheese thickens it as well.For a thinner soup, do not add cornstarch. Add more milk or stock until you reach your desired consistency.