In a large, heavy-bottomed pot or Dutch oven, heat the vegetable oil over medium heat. Once hot, gradually whisk in the flour to create a roux. Stir continuously for 20-30 minutes until the roux is a deep brown color (similar to chocolate), being careful not to burn it.
Add the diced onion, bell pepper, celery, and garlic to the roux. Cook for about 5-7 minutes, stirring frequently until the vegetables are softened.
Stir in the sliced sausage, cooking until browned, about 5 minutes.
Add the diced tomatoes (with their juice), chicken broth, bay leaf, thyme, cayenne pepper, paprika, salt, and black pepper. Bring the mixture to a gentle boil, then reduce the heat and let it simmer uncovered for 30 minutes.
After 30 minutes, add the okra and stir well. Allow it to simmer for an additional 10-15 minutes until the gumbo thickens slightly.
Finally, add the shrimp and cook for about 5 minutes or until they turn pink and opaque. Adjust seasoning if necessary, and remove from heat.
Discard the bay leaf before serving.
Notes
Serve over steamed white rice and garnish with green onions and parsley.