Heat the olive oil (and butter, if using) in a large pot over medium heat. Add the sliced leeks and garlic. Sauté for 4-5 minutes until softened and fragrant.
2 tbsp extra virgin olive oil, 1 tbsp unsalted butter, 1 large leek, 2 cloves garlic
Stir in the carrots and celery, cooking for another 3 minutes.
2 medium carrots, 2 celery stalks
Add the diced potatoes and sprinkle the flour over the vegetables. Stir to coat evenly and cook for 2 minutes to remove the raw flour taste.
2 large Yukon Gold potatoes, 1/4 cup all-purpose flour
Gradually pour in the chicken or vegetable broth, stirring constantly to avoid lumps. Bring to a boil, then reduce the heat to low and simmer for 15-20 minutes, or until the potatoes are tender.
5 cups chicken or vegetable broth
Stir in the diced pickles and pickle juice, allowing the soup to simmer for another 5 minutes. This infuses the broth with a bright, tangy flavor.
1 cup dill pickles, 1/2 cup dill pickle juice
While the soup is simmering, poach the salmon. Place the fillet in a shallow pan and cover it with water or broth. Add a slice of lemon and a few dill sprigs. Simmer gently over low heat for 10 minutes or until the salmon is cooked through. Remove, flake into large chunks, and set aside.
1 lb salmon fillet
Stir in the heavy cream, fresh dill, lemon zest, and lemon juice. Taste and adjust the seasoning with salt, pepper, and smoked paprika, if desired.
1/2 cup heavy cream, 1/4 cup fresh dill, 1 tbsp fresh lemon zest, 1 tbsp fresh lemon juice, 1/2 tsp smoked paprika
Ladle the soup into bowls, topping each with flaked salmon. Garnish with additional fresh dill, diced pickles, and a drizzle of olive oil or crème fraîche for an extra touch.