If you’re starting with store-bought stock, add some chicken bones – perhaps the carcass of a rotisserie chicken – to the pot. If you have well-flavored homemade stock, don’t worry about adding any bones, just continue with veggies.
Put stock, (bones if using), leek, carrots, parsnip, celery, onion, and allspice in a large pot. Bring it to a boil, then reduce heat, and simmer 30-40 minutes.
While the potatoes cook, chop the dill pickles finely. In a 4-cup measuring cup or similar sized bowl, whisk the sour cream and flour together until completely smooth. Set both of these aside for now.
Strain the stock, reserving the carrots and parsnip. Discard the other vegetables (and bones if you used any) and return the stock to the pot. Add the potatoes and garlic, and cook 15 minutes or so, until the potatoes are tender.
While the potatoes are cooking, grate the reserved carrots and parsnip, or chop them very finely. When the potatoes are fork-tender, return the grated carrots and parsnip to the pot, and then add the chopped dill pickles, dried dill weed, and pickle juice. Continue simmering the soup; keep it just under a boil.
Temper the flour/sour cream mixture: slowly add 1 cup of the hot broth from the pot to the bowl of flour/sour cream, stirring constantly. Whisk this until it’s smooth and creamy, adding stock as needed. When it’s completely smooth, add all this back to the pot, and stir until well combined. Keep the soup at a simmer, and do not let it boil. Simmer 5-10 more minutes to thicken the soup a bit.
Taste the soup, and adjust seasonings. Dill pickle soup may need more salt or none at all, depending on the saltiness of the pickles you used. A bit of pepper, hot paprika, or even cayenne, may bring out the flavors for you.