In a large pot, heat the vegetable oil over medium heat.

Add the flour and stir continuously to make a roux, cooking until it's dark brown, about 20 minutes.

Add the chopped onion, bell pepper, celery, and garlic to the roux and sauté until softened.

Stir in the sliced sausage and cook for an additional 5 minutes.

Add the diced tomatoes and chicken broth, mixing well.

Season with cayenne pepper, thyme, salt, and pepper.

Bring the mixture to a boil, then reduce heat and let it simmer for 30 minutes.

Add the sliced okra and shrimp to the pot.

Simmer for another 10 minutes until the shrimp are cooked through.

Serve hot, garnished with chopped green onions.