In a large heavy skillet or Dutch oven, heat the vegetable oil over medium heat. Gradually whisk in the flour to create a roux, stirring constantly until it turns a deep brown color, about 15-20 minutes.

Add the diced onion, green bell pepper, and celery to the roux. Cook for about 5 minutes, stirring frequently, until the vegetables are softened.

Stir in the minced garlic and cook for an additional minute until fragrant.

Gradually pour in the chicken broth, stirring continuously to avoid lumps. Add the diced tomatoes, Cajun seasoning, Worcestershire sauce, salt, black pepper, and cayenne pepper if using. Bring to a simmer.

Add the shrimp to the mixture and cook for about 5-7 minutes, or until the shrimp are pink and cooked through.

Serve the etouffee over cooked white rice, garnished with sliced green onions and chopped parsley.