Heat the oil in a large stockpot over medium-high heat. Add the mushroom, salt, carrot and onion and saute until the vegetables begin to soften, about 3 minutes. Add the broth, fish sauce and tamarind, bring to a boil and then reduce the heat and simmer until the vegetables are fully cooked, about 10 minutes. Add the bok choy and chicken and continue to simmer until the bok choy is cooked and the chicken is heated through, about 5 minutes. Ladle the soup into bowls and serve with a sprinkling of scallions.