In a large skillet, melt the butter over medium heat. Once melted, whisk in the flour to create a roux. Cook, stirring constantly, for about 5-7 minutes until the roux is a golden brown color.
Add the chopped onion, bell pepper, and celery to the skillet. 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. Bring the mixture to a simmer.
Add the diced tomatoes, Cajun seasoning, Worcestershire sauce, salt, black pepper, and cayenne pepper (if using). Stir well and let it simmer for about 10 minutes, allowing the flavors to meld.
Add the shrimp to the skillet and cook for 5-7 minutes, or until the shrimp are pink and cooked through.
Serve the shrimp étouffée over cooked white rice and garnish with sliced green onions.