In a large pot or Dutch oven, heat the vegetable oil over medium heat. Gradually add the flour, stirring constantly to make a roux. Cook for about 15-20 minutes until the roux turns a dark caramel color, but be careful not to burn it.
Once the roux is ready, add the chopped onion, green bell pepper, celery, and garlic. Cook for an additional 5-7 minutes until the vegetables are softened.
Stir in the shrimp and cook until they turn pink, about 3-4 minutes.
Gradually add the chicken broth while stirring to combine. Bring the mixture to a simmer and add the hot sauce, Worcestershire sauce, thyme, paprika, cayenne pepper, salt, and pepper.
Reduce the heat to low and let the mixture cook for about 10-15 minutes, stirring occasionally, until the sauce thickens.
Serve the shrimp étouffée over a bed of cooked white rice. Garnish with chopped green onions and parsley as desired.