Heat the olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the diced potatoes to the pot and stir well. Pour in the vegetable broth, ensuring the potatoes are covered. Bring to a boil, then reduce to a simmer. Cook for about 15 minutes, or until the potatoes are tender.
Once the potatoes are cooked, add in the diced dill pickles and fresh dill. Stir to combine and let simmer for another 5 minutes.
Use an immersion blender to blend the soup to your desired consistency. If not using an immersion blender, carefully ladle the soup into a regular blender, blend until smooth, and return to the pot.
Lower the heat, and stir in the heavy cream. Allow it to heat through for about 5 minutes, being careful not to let it boil.
Season with salt and pepper to taste.
Serve hot, garnished with extra dill if desired.