Combine ingredients. Add the condensed soups, milk, and chicken broth to a large saucepan; stir to blend. Add the diced cooked chicken, chopped green onions (only the white and light green), corn, mushrooms, and chiles (if using). Mix well and place over medium heat. Cook, stirring frequently, for about 6 to 8 minutes or until onions are tender.Season the chowder. Add salt, pepper, and the cheese; stir until the cheese is melted.Serve. Garnish with the reserved sliced dark green onions and serve with cornbread or crusty rolls.