Combine the potatoes, celery, onion, garlic, carrot, ham, and chicken broth in a stockpot. Bring to a boil, then cook over medium heat until potatoes are tender, about 10 to 15 minutes. Stir in salt and pepper. In a seperate 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 so that lumps don't form and until all of the milk has been added. Continue sitting over medium0low heat until thick, 4 to 5 minutes. Stir the milk mixture into the stock pot and cook soup until heated through. Top with cheddar cheese, chives, and bacon if desired.
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