1. Place the diced chicken in a medium mixing bowl. Add the kosher salt, Italian seasoning, mustard powder, paprika, and chili flakes, and toss to evenly coat the chicken. Set aside.
2. Heat a large Dutch oven or soup pot over medium heat. Melt the butter, then add the diced onions, carrots, and celery. Season with kosher salt to taste. Sauté, stirring occasionally, for 5-7 minutes. Add the minced garlic and cook for another 30 seconds.
3. Add the seasoned chicken to the pot and cook until no longer pink. Stir in the chopped thyme and rosemary.
4. Sprinkle the flour over the chicken and vegetables, stirring well to coat everything evenly.
5. Gradually pour in the chicken broth, half and half, soy sauce, and hot sauce. Add the uncooked rice and stir to combine. Increase the heat to medium-high to bring the mixture to a boil, then reduce heat to low and simmer for about 15-20 minutes, stirring frequently to prevent the rice from sticking to the bottom.
6. Taste the soup and adjust seasoning with more hot sauce, salt, or pepper as desired. Serve the soup in bowls, garnished with shaved Parmesan, cracked black pepper, and fresh parsley.