Sauté the aromatics: Heat the butter and olive oil in a heavy pot over medium heat.
Add onion, celery, and carrot. Cook until softened, about 6–8 minutes. Stir in the garlic and cook 30 seconds until fragrant.
Make a light roux: Sprinkle the flour over the vegetables and stir for 1 minute.
This thickens the chowder without making it gluey.
Add stock and simmer: Slowly whisk in the seafood stock to avoid lumps. Add potatoes, bay leaf, thyme, and paprika. Bring to a gentle simmer and cook 10–12 minutes, or until the potatoes are just tender.
Stir in dairy: Lower the heat.
Add the milk and cream, and bring back to a very light simmer. Do not boil after adding dairy.
Add seafood: Gently slide in the fish, shrimp, and clams. Simmer on low, 4–6 minutes, until the fish flakes and shrimp turn pink and opaque.
Finish with corn and herbs: Stir in the corn and half the parsley or chives.
Heat through for 1–2 minutes.
Season and serve: Remove the bay leaf. Taste and season with salt and pepper. Ladle into bowls, top with remaining herbs, and serve with lemon wedges and crusty bread or crackers.