Sauté the Sausage: Heat the olive oil in a large pot over medium heat. Add the turkey sausage slices and sauté for 3-4 minutes until lightly browned. Remove the sausage from the pot and set aside.
Sauté the Veggies: In the same pot, add the onion, celery, bell peppers, garlic, and chili pepper. Sauté for 5-7 minutes until the vegetables are soft and fragrant.
Add Chicken: Stir in the cubed chicken breast. Cook for 5 minutes, stirring occasionally, until the chicken is lightly browned on the outside.
Incorporate Tomatoes and Spices: Add the grated tomatoes, bay leaf, allspice, salt, and pepper to the pot. Stir well to combine and let the mixture cook for 3-4 minutes to release the flavors.
Add the Rice and Broth: Pour in the rinsed rice and chicken or seafood broth. Stir gently to ensure the rice is evenly distributed and submerged. Return the sausage to the pot. Bring the mixture to a boil, then reduce the heat to low. Cover the pot with a lid and let it simmer for 25 minutes, stirring occasionally.
Add the Shrimp: After 25 minutes, gently stir in the shrimp. Cover the pot and cook for an additional 3 minutes, or until the shrimp are pink and fully cooked, and the rice is tender.
Adjust Seasoning and Serve: Taste the Jambalaya and adjust the seasoning with additional salt and pepper, if needed. Remove the bay leaf before serving. Serve hot, garnished with chopped parsley or green onions if desired.