Start the base: Melt butter in a medium pot over medium heat. Add leek and carrots. Cook for about 5 minutes, stirring occasionally.
Cook the vegetables: Add potatoes, salt, pepper, and broth. Bring to a boil, then reduce heat, cover, and simmer for 10–15 minutes, until tender.
Add the salmon: Add salmon pieces and cook for 3–4 minutes, until just cooked through. Do not overcook.
Finish the soup: Stir in cream and dill. Heat gently for about 1 minute. Do not boil after adding cream.
Serve: Serve immediately, topped with extra fresh dill.