1. Heat the oil in a large pot over medium heat. Gradually whisk in the flour to make a roux. Cook, stirring constantly, until the roux is a dark brown color, about 15-20 minutes.
2. Add the onion, bell pepper, celery, and garlic to the roux. Cook, stirring often, until the vegetables are tender, about 5 minutes.
3. Stir in the sausage and cook for another 5 minutes.
4. Gradually whisk in the chicken broth. Add the okra, Cajun seasoning, thyme, and bay leaves. Bring to a boil, then reduce the heat and simmer for 30 minutes.
5. Add the shrimp and cook until they are pink and cooked through, about 5 minutes. Season with salt and pepper to taste.
6. Serve the gumbo over cooked white rice.