In a 5 to 6-qt Dutch oven melt butter over medium heat. Add onion, carrot and celery. Cook and stir 5 minutes or until tender. Add pickles and cook 2 minutes more.
Add broth, potatoes, and brine. Bring to boiling. Reduce heat and simmer, covered, 15 to 20 minutes or until potatoes are tender.
In a medium bowl whisk together sour cream and flour. Gradually add about 1 cup of soup to the sour cream mixture, whisking to combine. Add all the sour cream mixture back to the soup. Return to a simmer, stirring occasionally until thickened, 3 to 4 minutes. Season with dill, pepper and salt if desired. Garnish servings with pickle slices, dill, and pepper.
