Heat the butter in a large pot over medium heat and cook the onions, carrots, and celery until softened, about 4 minutes. Stir in the garlic and continue cooking for an additional minute.
Add basil, parsley, oregano, thyme, mustard powder, pepper, soy sauce, hot sauce, chicken breast, and 5 cups chicken broth to the pot. Gently bring just to a simmer, partly covered, and let the chicken cook through slowly for 15 to 20 minutes without boiling.
Remove the chicken breast and shred the meat using two forks, discarding the bones. Return the shredded chicken to the pot.
Meanwhile, prepare the rice by bringing 1 ½ cups chicken broth to a boil in a separate saucepan. Add the uncooked rice and return to a boil. Cover tightly, reduce heat to low, and simmer for 15 minutes.
Turn off the heat and let the rice rest, still covered, for 10 minutes to finish cooking and release any stuck grains.
Adjust the soup seasoning with salt if needed. To serve, spoon the cooked rice into bowls and ladle the hot soup over the top.
Garnish with fresh parsley and enjoy your comforting, easy-to-make chicken and rice soup.