Melt butter in a large soup pot over medium heat. Add diced onions, carrots, and celery. Sauté for 4 minutes to soften, then incorporate minced garlic and cook for an additional minute.
Stir in the dried basil, parsley, oregano, thyme, mustard powder, and pepper, followed by the soy sauce, hot sauce, chicken breasts, and 5 cups chicken broth.
Bring to a gentle simmer and partially cover the pot. Cook the chicken until tender, about 15–20 minutes. Remove and shred the meat using two forks, discarding the bones. Return shredded chicken to the pot. During this time, prepare the rice separately.
In a medium saucepan, bring 1 ½ cups chicken broth to a boil. Add the rice and ensure it’s submerged. Once boiling resumes, cover tightly, reduce to a low simmer, and cook for 15 minutes. Turn off the heat and let the rice sit, covered, for 10 minutes to loosen any grains from the bottom. This produces about 2 ¼ cups of rice.
Taste the soup and add salt if needed. For serving, place a portion of rice in each bowl, then ladle the soup over it. Combine both in the pot only if you expect no leftovers. Garnish with chopped parsley before serving.