Sauté the aromatics: In a large soup pot, heat the butter and olive oil over medium heat. Add diced onion, garlic, celery, and carrot. Cook until softened, about 5 minutes.
Add potatoes and broth: Stir in the diced potatoes and pour in the stock. Bring to a boil, then reduce to a simmer. Cook for 12–15 minutes or until potatoes are fork-tender.
Blend (optional): For a thicker chowder, use an immersion blender to lightly blend part of the soup. Or transfer 1 cup to a blender and pulse, then return to the pot.
Add cream and seasonings: Stir in the cream, milk, smoked paprika, thyme, salt, and black pepper. Let the soup gently simmer for another 5 minutes.
Add lobster: Gently fold in the cooked lobster meat and heat through for 2–3 minutes; do not boil.
Serve: Ladle into bowls, garnish with chopped parsley, and enjoy with crusty bread or oyster crackers.