In a large pot or Dutch oven over medium heat, heat the avocado oil and toasted sesame oil. Add the white parts of the green onion, mushrooms, garlic, ginger, and salt to the pot. Sauté until the veggies are tender, about 3 minutes.
Add the baby bok choy and sauté, stirring, until tender, about 2 more minutes.
Next, add the broth, coconut aminos, rice vinegar, fish sauce, and lime juice to the pot. Stir to combine. Bring to a simmer.
Once simmering, add the wontons and cilantro and stir to combine. Cook until the wontons are tender; about 2 minutes. The wontons will float to the top when done.
Serve in bowls with a drizzle of chili oil (if desired) and top with the reserved green parts of the green onion.