Warm the oil in a heavy pot over medium heat. Sprinkle in the flour, whisking constantly to form a roux.
Stir and cook the roux until deep peanut-butter brown, 12–18 minutes, lowering heat if it darkens too fast.
Add onion, bell pepper, and celery. Cook, stirring, until softened and glossy, about 5 minutes.
Stir in the garlic and cook 1 minute until fragrant.
Add the andouille and cook until lightly browned at the edges, about 3 minutes.
Mix in tomatoes, Creole seasoning, thyme, smoked paprika, crushed bay leaf, and Worcestershire. Cook 2 minutes.
Gradually whisk in the warm chicken stock until smooth. Bring to a gentle boil, then reduce to a simmer.
Add the okra. Simmer uncovered 25–30 minutes, stirring occasionally. Adjust thickness with a splash of stock if needed.
Season with salt, black pepper, and hot sauce to taste.
Stir in the shrimp and cook just until pink and curled, 3–5 minutes. Remove from heat and rest 5 minutes.
Finish with green onions and parsley. Sprinkle filé powder in individual bowls if using, and serve over rice.