In a large pot over med-high heat, heat 2 Tbsp. of the olive oil. Stir in chicken pieces and sausage pieces and cook for about 2 to 3 minutes. Stir in the rest of the oil, bell peppers, celery, onion, and jalapeno. Saute until onion is soft and somewhat see-through, or for about 6 more minutes. Add in garlic and continue to saute for an additional 1 minute. Stir in flour and cook for about 1 minute. Stir in chicken broth, 1 cup at a time. Add in crushed tomatoes, white rice, Cajun seasoning, dried bay leaves, and dried thyme. Cook until the soup starts to simmer.

Reduce heat to med-low and simmer for 15 minutes, stirring occasionally to keep rice from burning. Rice should be cooked all the way by this point.

Add in shrimp and cook for an additional 5 minutes. Season with salt and pepper.

Garnish with parsley or other desired topping and serve warm.