Wash and peel potatoes. Cut into bite sized pieces.
Wash, peel and grate the carrot.
Chop onion and celery finely.
Add and mix together potatoes, celery, onion, carrot, chicken broth, salt and vinegar into a Dutch oven over medium heat.
Bring to a boil. Reduce heat and simmer for 20 minutes.
Whisk together the milk and flour in a separate bowl.
Remove soup from heat and add the milk/flour mixture.
Return to heat and simmer for 10 minutes, stirring occasionally, until thickened.
Add cheeses and continue cooking until desired thickness.
Add to bowls and garnish with your favorite toppings: sour cream, chopped ham or bacon, and/or green onion.