In a large saucepan combine broccoli, corn, water, onion, and thyme. Bring to boiling. Reduce heat and simmer, covered, for 8 to 10 minutes or until vegetables are tender. Do not drain.
Stir milk, chicken or turkey, potato soup, the 3/4 cup cheddar cheese, and pepper into vegetable mixture. Cook and stir over medium heat until cheese melts and mixture is heated through. Sprinkle each serving with the remaining cheddar cheese. Makes 4 servings.