In a large stock pot, combine potatoes, onion, carrots, peas, ham and chicken broth. Bring to a boil, lower heat to medium, and let cook until potatoes are soft (about 15-20 minutes for mine). Add salt and pepper, if desired.In a small saucepan, melt butter over medium-low heat. Whisk in the flour and continue to stir constantly until the mixture thickens (about 1-2 minutes).Slowly add the milk to the butter/flour mixture, stirring the entire time so that you don't get any lumps. Continue to stir until the mixture thickens once again (takes about 3-5 minutes).Add in the cheese to the butter/flour/milk mixture and stir until it's completely melted.Pour the cheese mixture into the stock pot with the vegetables and ham and stir until completely incorporated. It will get thicker as it cools.