Combine diced potatoes, carrots, celery and onions with chicken broth in a large stockpot and season with salt and pepper to taste.
Cover pot and bring to a boil over medium-high heat (it will take about 10 minutes to reach a boil), once it reaches a boil reduce heat to medium and continue to cook about 15 - 20 minutes longer until potatoes are very soft when pierced with a fork.
Meanwhile, in a medium saucepan melt butter over medium heat, add flour and cook for 1 minute while whisking constantly. While whisking, slowly add milk and cook, stirring constantly until mixture begins lightly bubble and thicken.
Ladle soup into serving bowls, top each serving with bacon or ham, cheddar cheese and green onions (Note that the soup will thicken as it rests so if you happen to have left overs you can thin with a little water or milk).
Creamy and comforting!....Yum, Enjoy!
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