Warm a heavy pot over medium-low. Whisk oil and flour until a deep brown roux forms, 20–25 minutes.
Stir in onion, bell pepper, and celery. Cook until softened, 6–8 minutes, stirring often.
Add garlic and cook 1 minute until fragrant.
Mix in the sliced andouille. Cook 4–5 minutes to render lightly and pick up roux flavor.
Sprinkle in Cajun seasoning, smoked paprika, thyme, salt, and pepper. Stir 30 seconds to bloom spices.
Gradually whisk in the chicken broth until smooth. Add the okra and bring to a gentle simmer.
Lower heat and simmer uncovered 30–35 minutes, stirring now and then to prevent sticking.
Stir in Worcestershire and hot sauce. Taste and adjust salt or Cajun seasoning as needed.
Add shrimp and simmer 3–4 minutes until just pink. Turn off heat; fold in parsley and filé powder, if using.
Ladle gumbo over warm rice and garnish with green onions. Serve hot.