Grate all the cheese, then save a small amount aside to sprinkle on top of the casserole.
Cut the squash into medium thin slices, the onion in very thin slices.
Cook squash/onion the following way: place cut squash and onion in a pan of cold water. Bring to a boil, then immediately remove from stove and drain well.
Combine squash/onion with most of the shredded cheese, 1/2 stick of butter, 1 cup of seasoned bread crumbs. This will form a thick "pasty" mixture.
Add 1 beaten egg (or substitute). If mixture is too runny, add a little more bread crumbs. If too dry, add a little milk.
Add to mixture a heavy "dash" of Worcestershire, 1/2 to 1 tsp of sugar (to taste), a dash of Tabasco sauce, a good dash of garlic powder, then salt and pepper to taste. Mix well.
Spoon mixture into the buttered baking dish. Sprinkle top lightly with bread crumbs and the small amount of grated cheese that was set aside. Cut small amount of butter into a few thin slices and "dot" on top of casserole.
Bake at 350 degrees F for 35 minutes. Let cool slightly before serving to "set" the casserole.