First, cook the greens by bringing a pot of water to a boil. Add greens and boil gently for 15 minutes, stirring occasionally to submerge greens if necessary. Drain in colander.
While greens are boiling, melt butter in large saucepan or soup pot. Over medium-low heat, sauté mushrooms in butter until tender, about 7-10 minutes, adding scallions to the pot during the last 2 or so minutes. Add flour and stir just until flour is cooked, a couple of minutes; mixture will become dry and pasty when flour is added.
Add chicken broth a little at a time, stirring between additions, to loosen up the pasty flour-mushroom mixture. Add milk, salt (may need less if chicken broth is salty), pepper and nutmeg, cooking and stirring until thickened, about 5-10 minutes or so (soup mixture must come to a gentle boil to thicken properly).
Add cream cheese and Swiss cheese, and cook and stir until cheeses are melted and smooth, a couple of minutes. Stir in cooked greens. Heat through, stirring gently, and taste to see if any additional seasonings are needed, such as more salt, ground pepper or ground nutmeg (nutmeg will be a very subtle flavor so should not overpower). If so, add and stir. Serve hot.