Heat the oil in a medium Dutch oven or sauté pan over medium heat. When the oil is hot and shimmering, add the onion and garlic and cook for about 5 minutes or until the onions are soft and translucent and the garlic is fragrant. Add the ginger and butternut squash and cook for 1 minute, then stir in the chicken broth, soy sauce, fish sauce, and crushed red pepper. Bring to a simmer.
Slice the chicken breasts in half crosswise (this will help them cook faster) and add them to the pan. Cover the pan with a lid and cover for 20 minutes or until the chicken is cooked through and the squash is just tender.
Transfer the chicken to a cutting board and shred the meat with two forks. Return the shredded chicken to the pan and add the rice noodles. Cook, stirring occasionally, until the noodles have softened, about 3 minutes. Stir in the scallions and bok choy and cook for 1 to 2 minutes or until the bok choy leaves have wilted and the stems are slightly softened. Taste the noodles and season with a little salt if needed.
Ladle the noodles and broth into bowls and serve garnished with chopped cilantro and peanuts, a drizzle of Sriracha if you love heat, and lime wedges.