Melt butter in a large pot over medium heat. Add onion, garlic, celery, and carrot. Cook for 5–7 minutes until softened.
Stir in the flour and cook for 2 minutes until lightly golden.
Gradually whisk in the broth, then add cream, milk, tomato paste, bay leaf, paprika, cayenne, lemon juice, salt, and pepper. Bring to a gentle boil.
Reduce heat and simmer for 15 minutes, stirring occasionally.
Add shrimp and crab meat. Cook for 5–7 minutes until shrimp are pink and fully cooked.
Remove bay leaf. Blend the bisque using an immersion blender until smooth, or partially blend for a chunkier texture.
Adjust seasoning and serve hot, garnished with fresh parsley.