In a large skillet or Dutch oven, heat the vegetable oil over medium heat. Gradually whisk in the flour to create a roux. Cook, stirring constantly, until the roux is a deep golden brown, about 10-15 minutes.
Add the diced onion, bell pepper, and celery to the roux. Sauté for about 5 minutes until the vegetables are softened.
Stir in the minced garlic and cook for an additional minute until fragrant.
Gradually add the chicken broth, stirring constantly to prevent lumps. Then add the diced tomatoes, Cajun seasoning, Worcestershire sauce, bay leaf, salt, and pepper. Bring to a simmer.
Reduce the heat to low and let the mixture simmer for about 15 minutes, stirring occasionally.
Add the shrimp to the skillet and cook for an additional 5-7 minutes, or until the shrimp are pink and cooked through.
Remove the bay leaf and adjust seasoning if necessary.
Serve the etouffee over cooked white rice and garnish with sliced green onions and chopped parsley.