In a large pot, melt the butter over medium heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes.
Add the diced carrots and potatoes to the pot. Sauté for an additional 5 minutes, stirring occasionally.
Pour in the chicken or vegetable broth, bring to a boil, then reduce the heat to a simmer. Cover and cook for 15 minutes or until the vegetables are tender.
Stir in the chopped dill pickles, pickle juice, dried dill, salt, and pepper, and let the soup simmer for another 5 minutes.
For a creamier texture, use a blender to puree a portion of the soup, then return it to the pot. Alternatively, you can leave it chunky if you prefer.
Stir in the heavy cream and heat the soup until warmed through, about 3-5 minutes. Adjust salt and pepper to taste.
Serve hot in bowls, garnishing with additional dill or chopped pickles if desired.