Fill a large pot with water, and add the two cans of beef broth. This will be the cooking water for the potatoes. While the potatoes are cooking, sauté the chopped onion, shallot and green pepper in the butter. I usually start with the onion, and once they have softened a bit, then add the shallot and green pepper. Set aside. Once the potatoes have cooked almost the whole way through, drain, but set aside about two cups of the cooking water. Add the can of cream of mushroom soup, and two cups of milk. Then add a cup of the potato cooking water. I usually end up adding the last cup of milk, along with more cooking water, but like to do it in stages so I can see how thick or thin the soup is becoming. Add the cheese and seasoning, and let them melt into the soup. Bring the soup briefly to a boil so the flavors meld, but then lower the heat.