1) Combine the potatoes, celery, onion, ham and water in a stockpot. Bring to boil, then cook over medium heat until potatoes are tender, about 10 to 15 minutes. Stir in the chicken bouillon, salt and pepper.
2) Optional: For the ham and water, I substitute ham stock made by boiling the water and ham bone for several hours.
3) In a separate saucepan, 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 to 5 minutes.
4) Stir the milk mixture into the stockpot, and cook soup until heated through. Serve immediately.