Heat a splash of olive oil in a large pot over medium heat. Add the sliced leek and sweat for about a minute until softened.
Add the potatoes, lemon slices, and stock. Cover and bring to a boil. Simmer for 10 minutes.
Add the tenderstem broccoli and cream. Cover and cook for another 2 minutes.
Add the fish and dill, then cover again and cook for a final 2 minutes, or until the fish is opaque and flakes easily with a fork.
In a small bowl, mix the cornstarch with a tablespoon or two of cold water to make a slurry. Stir it into the pot and let it simmer for another minute to slightly thicken the broth.
Season with salt and white pepper to taste. Serve in deep bowls with a drizzle of olive oil, extra white pepper, dill, and lemon slices.