Cook your rice noodles according to the package directions. Rinse them with warm water and set them aside.

Add 2 tablespoons of the oil and the garlic to a large pot and turn the heat on medium-low. Keep moving the garlic around as it starts to sizzle, turning it often until it turns light golden brown, about 2 to 3 minutes once the oil is hot. Remove it to a plate with a slotted spoon and set it aside.

Turn the heat to medium, add the last tablespoon of oil to the pot and add the shallots and ginger. Cook, stirring often, until the shallots are soft and lightly browned in spots, about 5 minutes. Add the hoisin and cook it for about 1 minute. Add the stock or water and bring it to a boil, then turn the heat down to a simmer, add the chicken pieces and scallion whites and cook until chicken is cooked through and tender. The thickest part of the chicken should register about 160°F on an instant read thermometer. Boneless breasts may take about 10 to 15 minutes, large bone-in thighs may need 25 to 30 minutes. Turn the heat off, remove the chicken to a plate and use two forks to shred the meat, discarding the skin and bones if needed. If there is a layer of fat on top of the broth, you can remove it with a spoon, if desired. Remove and discard the ginger, return the shredded chicken to the pot and stir in the sesame oil and scallion greens. Taste the broth and season it with salt and/or soy sauce, if desired (the amount will depend on the saltiness of the broth used). If the soup has cooled, heat it on medium until it returns to a simmer before serving.

To serve, divide the noodles into four soup bowls and ladle in the hot broth and chicken. Top each serving with some crispy garlic and torn cilantro. Serve with lime wedges for squeezing and some spicy chili-garlic paste on the side.