In a large pot or Dutch oven, heat the vegetable oil over medium heat. Slowly whisk in the flour and cook, stirring continuously, to create a roux. Keep cooking until the roux is a deep brown color, about 15-20 minutes. Be careful not to burn it.
Once the roux is ready, add the chopped onion, green bell pepper, and celery to the pot. Cook for about 5 minutes until the vegetables are softened.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Gradually pour in the seafood or chicken broth, stirring constantly to prevent lumps. Add the diced tomatoes, okra, Worcestershire sauce, Cajun seasoning, thyme, bay leaf, cayenne pepper, salt, and pepper. Mix well.
Bring the mixture to a boil, then reduce the heat and let it simmer uncovered for about 20-30 minutes. Stir occasionally.
After the gumbo has thickened, add the shrimp and cook for an additional 5-7 minutes until the shrimp are pink and opaque.
Remove the bay leaf before serving.
Serve the gumbo hot over cooked white rice and garnish with sliced green onions.