Warm a large pot over medium heat. Add the butter and olive oil. When the butter melts, add onion, celery, and carrot.
Cook, stirring occasionally, until softened and translucent, about 6–8 minutes.
Add garlic, salt, pepper, and smoked paprika. Cook 30 seconds, just until fragrant. Drop in the bay leaf.
Pour in the stock and bring to a gentle simmer.
Stir in the potatoes. Simmer uncovered until the potatoes are just tender, 10–12 minutes.
Add the corn and cream. Return to a gentle simmer. Do not boil once the cream is in, or the chowder can curdle.
Gently nestle the salmon pieces into the pot.
Simmer on low until the fish is just cooked through and flakes easily, 5–7 minutes. Avoid stirring too much so the salmon stays in nice pieces.
Remove the bay leaf. Stir in lemon juice and dill.
Taste and adjust with more salt, pepper, or lemon as needed.
Ladle into bowls and garnish with chives if you like. Serve hot with crusty bread or oyster crackers.