Melt butter in a large pot over medium heat. Add onion, garlic, celery, and carrot. Sauté for 5–7 minutes, stirring occasionally, until tender and fragrant.
Sprinkle flour over the vegetables and stir constantly for about 2 minutes until fully absorbed and lightly golden.
Gradually whisk in seafood or chicken broth until smooth. Stir in heavy cream, milk, seafood stock, tomato paste, bay leaf, paprika, cayenne, salt, and pepper. Bring to a gentle boil, then lower heat and simmer for 15 minutes.
Add shrimp and crab meat to the pot. Cook for 5–7 minutes, stirring occasionally, until the shrimp are pink and cooked through.
Remove and discard the bay leaf. Use an immersion blender to puree the bisque until smooth and creamy, or leave it slightly chunky if preferred.
Taste and adjust seasoning if needed. Ladle hot bisque into bowls, garnish with chopped parsley, and serve immediately.