Melt butter in a large pot over medium heat. Saute chicken, stirring frequently, until chicken is browned on all sides. Remove chicken to plate.
Add carrots, celery, red pepper, onion, and jalapeno (or green chilies) to pan and cook, stirring frequently, until veggies are softened. Stir in garlic and ham and cook for another few minutes.
Stir in the flour to the veggie mixture and continue to stir and cook for 2 to 3 minutes until flour is absorbed and cooks a bit.
Stir in chicken broth, corn, chicken, salt and pepper and bring mixture to a low boil. I usually add an additional 2 or so cups of water depending on the ratio of broth to veggies/chicken. Use your judgement and add enough water to your liking. Allow the soup to simmer/boil until the vegetables are tender and chicken is completely cooked through, about another 15 to 20 minutes depending on how well cooked everything was in the first couple of steps.
Stir in the cream and cheese until the cheese is melted. Adjust seasoning and add more salt and pepper and even cheese if desired. Simmer over low heat until ready to serve.