In a large Dutch oven, heat the vegetable oil over medium heat. Add the onions, bell peppers, and celery and season with the salt and cayenne. Cook, stirring, until the vegetables are wilted, about 5 minutes. Add the sausage and cook, stirring, for 2 minutes. Add the bay leaves, tomatoes, garlic, and crawfish and cook, stirring, for 2 minutes. Add the rice and cook, stirring, for 2 minutes, then add the broth and bring to a boil. Reduce the heat to medium-low, cover, and cook until the rice is tender and most of the liquid is absorbed, 25 to 30 minutes.
Stir in the green onions, remove the bay leaves, and serve hot.
Yield: 6 to 8 servings