Cook the potatoes in boiling salted water until just fork tender; drain.
Brown the lamb in a nonstick skillet (add a little oil if you need to but it may not need it- lamb mince varies in the amount of fat).
When the lamb is browned, drain off excess fat leaving just a tiny bit and add the onions, carrots, marjoram, garlic, black pepper, and salt, cooking just till the onions are tender.
Stir in the broth, green beans, ground mustard, Worcestershire sauce, kitchen bouquet and tomato paste, and simmer until green beans are tender.
While the mix with beans is finishing up, mash the potatoes and stir in the egg, butter, and salt and black pepper to taste.
Place the meat mixture in the bottom of a 2 quart buttered/pam sprayed casserole and top with the mashed potato mix.
Sprinkle with grated cheese.
Place in the oven and bake for 30 minutes or more (until the top is lightly browned).