Season the chicken pieces generously with Cajun seasoning, salt, and black pepper.

Heat vegetable oil in a large skillet over medium-high heat. Add the chicken pieces in batches and brown on all sides. Remove chicken from the skillet and set aside.

In the same skillet, add the chopped onion, bell pepper, and celery. Sauté over medium heat until softened, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the tomato paste and cook for 1 minute. Pour in the crushed tomatoes and chicken broth. Add dried thyme, oregano, cayenne pepper (if using), bay leaf, salt, and black pepper to taste. Bring the sauce to a simmer.

Return the browned chicken to the pot or Dutch oven. Stir to coat the chicken with the sauce. Bring back to a simmer, then reduce heat to low, cover, and simmer for 30-40 minutes, or until the chicken is cooked through and tender.

If you prefer a thicker sauce, remove the chicken from the pot and set aside. Increase the heat to medium and simmer the sauce uncovered for 10-15 minutes, or until it reduces to your desired consistency. Alternatively, you can mix 1 tablespoon of cornstarch with 2 tablespoons of cold water to make a slurry and stir it into the simmering sauce in the last few minutes of cooking.

Return the chicken to the sauce if removed. Remove the bay leaf. Taste and adjust seasoning if needed. Serve hot over cooked rice. Garnish with fresh parsley or green onions, if desired. Add hot sauce to taste for extra heat.