Heat the avocado and toasted sesame oil in large pot or Dutch oven over medium heat. Add the onion, garlic, white part of the green onion, ginger, salt and pepper and cook, stirring, until the onions are tender, about 5 minutes.
Add the broth, tamari, rice vinegar, turmeric and coriander and bring to rapid simmer.
Once simmering, add the chicken the rice and reduce the heat to a light simmer, about medium-low heat. Cook, covered, until the rice is tender and the chicken is cooked through, about 20 minutes.
Using tongs, transfer the cooked chicken to a sheet pan and using two forks, shred the chicken. Alternatively, you can dice the chicken into bite-sized pieces.
Add the chicken back to the soup along with the bok choy, the green parts of the green onion, and the lime juice. Stir to combine. Continue to cook, uncovered and simmering lightly, until the bok choy stems are tender, 3 to 4 minutes.
To serve, ladle the soup into bowls and finish with a drizzle of chili oil, a sprinkle of toasted sesame seeds, and some fresh cilantro. Serve with a wedge of lime for squeezing.