Add the olive oil to a large pot on medium-high heat. Add the onion and carrot once the oil is hot. Sauté for 5 minutes.
Add the remaining ingredients except for the sour cream and flour. Bring to a boil then reduce the heat to medium-low. Simmer for 15-20 minutes, or until the potatoes are tender.
Mix the flour into the sour cream until you have a smooth mixture. Stir it into the soup and cook the soup for another 5 minutes. Season with salt & pepper to taste. Garnish with extra fresh dill if desired.
This soup can turn out a bit salty for some people (depending on the salt in the pickle juice) so I suggest using low-sodium chicken broth if that's a concern for you.
If using dried dill, start with 1 teaspoon and work your way up from there if needed.