In a large pot or skillet, warm 2 tablespoons oil over medium heat. Add the sausage links and cook for about 5 minutes on each side, until light golden brown. Transfer to a plate lined with a paper towel and set aside. Scrape out any bits of sausage that were left in the pot and discard.
To the same pot, add the remaining tablespoon of oil. Add the onion, celery, bell pepper, and jalapeño. Cook for about 5 minutes.
Next, add the cajun seasoning, thyme, and garlic. Continue to cook for another 5 minutes, or until the vegetables are slightly tender. Pour in the crushed tomatoes, broth and rice. Bring to a boil then reduce to a simmer. Cover and cook for 15-20 minutes, until the rice is cooked through.
Lastly, stir in the okra. Cover and cook for 5 minutes more. Add the beans and sausage to the pot, stir everything together and cook until heated through. Seasoning with salt & pepper. Serve warm with desired garnishes and enjoy!