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 slowly while stirring. Once incorporated, cook for 1 minute while stirring with a wooden spoon constantly. While stirring, slowly add milk and cook, stirring constantly until mixture begins lightly bubble and thicken.
Once potatoes are soft add thickened milk mixture to potato soup mixture and stir (potatoes should start breaking down into soup, if not cook a few minutes longer). Add sour cream and mix well.