Boil the potatoes until soft, but not disintegrating. Drain. Put the potatoes into a deep bowl and add the butter (in chunks), salt, white pepper, and hot milk. Using a heavy wire whisk or potato masher, mash the potatoes, leaving small lumps. Set aside, covered.
In a skillet over medium heat, saute the onions and bell peppers until soft, but not browned.
Break the ground beef into the pan and add the salt, pepper, Worcestershire, soy sauce, marjoram, dry mustard and about 2 Tbs. water. Saute, breaking up the clumps of beef with a kitchen fork. Continue to cook, stirring frequently, until most of the liquid in the pan is gone. Remove from heat.
Cover the bottom of a 4x9x3 ceramic or glass baking dish with the squash, zucchini, and/or corn. Cover that with a thin layer of mashed potatoes. Using a slotted spoon, transfer the beef mixture to the baking dish. Top it with the remaining creamed potatoes. (Tip: spoon the potatoes into the center of the dish in a big pile and spread it out to the edges, to minimize mixing with the meat.)
Sprinkle the cheese on top and bake in a preheated 350-degree oven until the cheese just browns--35-40 minutes.
Allow to cool 10 minutes before serving, so that you can cut out large cubes. (Also, the heat of the interior will be lava-like for awhile.)