
If I have a ham bone, I use it in this soup and simmer it in the broth before adding the potatoes. I've included the additional directions within the recipe. But the soup still tastes great without a ham bone.
In a large, heavy stockpot over medium low heat, heat the olive oil and saute the onions and celery for 8 minutes. Stir in the garlic and saute for 1 minute.
Stir in the water, diced ham, and ham bone. Bring to a boil and then simmer on low for 30 minutes. Remove the ham bone. (If you're not using a ham bone, just go directly to the next step)
Stir in the potatoes and again bring to a boil and then simmer for 30 minutes or until the potatoes are soft. Add salt and pepper to taste.
In a small saucepan, melt the butter over low heat and slowly whisk in the flour, stirring until it begins to thicken. Slowly, while whisking, stir in the milk, making sure that no lumps form and the milk doesn't burn. Cook, stirring continuously, for five minutes or until thick.
Slowly stir the roux into the stockpot with the ham and veggies. If necessary, use 1-2 cups of chicken broth to thin the soup to a desired consistency. Once it's heated through, serve immediately.
Note: This is soup, not a super-thick chowder. If you want a really thick chowder-y type soup, double the recipe for the roux (butter and flour) but don't add any extra milk.