Melt butter in a large Dutch oven.
Add carrots, leeks, celery, bell peppers, onions and mushrooms.
Cook over medium heat until veggies are tender, about 5-8 minutes.
Add flour and cornstarch and stir into mixture.
Slowly work in chicken broth.
Add potatoes and cook about 8-10 minutes over low to medium heat, or until potatoes are fork tender.
This mixture will thicken so continue stirring almost constantly so veggies don’t stick to the bottom of the Dutch oven.
If necessary, add a cup of water to pot if veggies start to stick.
Add green beans, corn and peas and cook an additional 3-5 minutes.
Slowly stir in milk or half-and-half and seasonings.
Add cheese and turn heat to low.
Continue stirring until cheese melts.
Do not allow cheese to boil.
Add ham.
Check seasonings.
Add additional salt and pepper, if desired.