In a stock pot or Dutch oven, heat the oil over medium heat. Add the celery, onion, bell peppers, jalapeno, and garlic. Cook for 3 - 4 minutes, stirring occasionally. Stir in the Andouille sausage and cook for an additional 3 - 4 minutes, again stirring occasionally until the vegetables have softened.
Add the chicken broth, tomato sauce, herbs, spices, and bay leaves. Simmer for 12 minutes.
Add in the rice, cover and continue simmering for approximately 15 minutes.
Stir in the shrimp. Cover and simmer for another 5 - 7 minutes.
Turn off heat and let stand covered for another 10 minutes. Remove bay leaves, plate and serve. Optional: Top with chopped parsley for garnish.