In a large skillet, heat the vegetable oil over medium heat. Gradually whisk in the flour to create a roux. Stir the mixture continuously for about 10-15 minutes until it becomes a deep golden brown color.
Add the chopped onion, green bell pepper, and celery to the roux. Cook for about 5 minutes until the vegetables soften.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the shrimp to the skillet and cook for about 2-3 minutes until they begin to turn pink.
Pour in the chicken broth and add the Worcestershire sauce, Cajun seasoning, cayenne pepper, salt, and black pepper. Stir well to combine.
Bring the mixture to a simmer, reduce the heat to low, and let it cook for another 10-15 minutes, stirring occasionally, until the sauce thickens.
Taste and adjust seasoning as necessary.
Serve the shrimp étouffée over a bed of cooked white rice. Garnish with sliced green onions and chopped parsley.