In a large pot, heat the olive oil or butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Add the diced potatoes to the pot, followed by the vegetable or chicken broth. Bring to a boil, then reduce to a simmer. Cook until the potatoes are tender, about 15-20 minutes.
Once the potatoes are cooked, you can use a blender or immersion blender to puree half of the soup for a creamy texture, leaving some chunks for a better mouthfeel.
Stir in the sour cream, chopped dill pickles, pickle juice, and fresh dill. Mix well.
Season the soup with salt and pepper to taste. Cook for an additional 5 minutes on low heat to warm through.
Serve hot, garnished with additional dill or pickles if desired.