Ham and Potato Soup

(Dave said this was THE BEST SOUP I've ever made!)

3 1/2 c peeled and diced potatoes (unless using red, then don't peel)
1/3 c celery, diced
1/3 c onion, chopped
1/3 c carrots, chopped (optional)
1 c cooked ham, cubed
3 1/4 c water
2 T chicken bouillon granules
1/2 t salt, or to taste
1 t pepper
5 T butter
5 T flour
2 c milk (or half & half, or cream)
1 c cheddar cheese, shredded

Combine the potatoes, celery, onion, ham, and water in a stockpot.  Bring to a boil, then cook over medium heat until potatoes are tender, about 10-15 minutes.  Stir in the chicken bouillon, salt, and pepper.

In a separate sauce pan, melt butter over medium-low heat.  Whisk in flour with a fork, and cook, stirring constantly until thick (about 1 minute).  Slowly stir in milk as not to allow lumps to form, until all of the milk has been added.  Continue stirring over medium-low heat until thick, 4-5 minutes.

Stir the milk mixture into the stockpot, and cook soup until heated through.  Put the shredded cheese in the soup to warm, or serve on top of each bowl.  Serve immediately.