Heat the vegetable oil in a large pot or Dutch oven over medium heat. Gradually whisk in the flour and stir continuously for 20-30 minutes until a deep brown color is achieved.
Add the sliced andouille sausage to the pot and cook for 5 minutes until browned.
Add the diced onion, green bell pepper, celery, and minced garlic. Cook for 5-7 minutes until softened.
Stir everything together, ensuring the roux coats the sausage and vegetables evenly.
Pour in the chicken broth, add the undrained diced tomatoes, sliced okra, Cajun seasoning, dried thyme, bay leaves, salt, and pepper. Stir well and bring to a boil, then reduce heat to low.
Let the gumbo simmer for 30 minutes, stirring occasionally. After 30 minutes, add the peeled and deveined shrimp and cook for an additional 5 minutes until shrimp are pink and cooked through.
Remove bay leaves before serving.
Notes
Allow the gumbo to rest after cooking to enhance flavors. Adjust seasoning to taste.