Start by melting butter in a large pot over medium heat. Add diced onions, carrots, and celery, cooking until they begin to soften, about 4 minutes. Stir in minced garlic and cook for an additional minute until fragrant. Mix in the dried herbs, mustard powder, pepper, soy sauce, hot sauce, chicken breast, and chicken broth. Lower the heat to maintain a gentle simmer and partially cover the pot. Let the chicken cook slowly for 15 to 20 minutes until fully cooked through but tender. Remove the chicken and shred it carefully with two forks, discarding any bones, then return the shredded chicken to the pot. While the soup simmers, prepare the rice separately. Bring 1 ½ cups chicken broth to a boil in a medium saucepan, add the rice, cover, and reduce the heat to low. Cook for 15 minutes, then turn off the heat and let it rest covered for 10 minutes to finish steaming. Taste the soup, adding salt if needed. Serve by spooning cooked rice into bowls and ladling the soup over the top. Garnish with fresh parsley before serving.