Preheat oven to 350° F. Cut four 12x12-inch squares of aluminum foil.
Divide butter, brown sugar, vinegar, broth, rosemary, thyme and mushrooms among foil squares. Place onions on top of mushroom mixture; draw corners of foil together to seal.
Place foil packets in a baking pan and bake until onions are soft, about 40 minutes. Transfer onions and mushrooms to serving plates, reserving the cooking liquid. Set aside.
Heat liquid in a saucepan and stir in ham, green onions and tomato. Season with salt and pepper to taste; heat through. Serve alongside onions and mushrooms.Servings: 4