Cook rice noodles as per package instructions. Rinse with warm water and set aside.
In a large pot, heat 2 tablespoons oil on medium-low. Add garlic. Stir frequently until golden brown (2-3 minutes once oil is hot). Remove with a slotted spoon and set aside.
Increase heat to medium. Add remaining oil, shallots, and ginger. Cook until shallots are soft and lightly browned (about 5 minutes).
Add hoisin sauce, cook for 1 minute. Then add stock/water and bring to a boil.
Reduce to a simmer. Add chicken and scallion whites. Cook until chicken is cooked through (160°F). Time varies: 10-15 minutes for boneless breasts, 25-30 minutes for bone-in thighs.
Turn off heat. Remove chicken, shred it, and discard skin/bones if necessary. Skim off any fat from broth if desired. Remove and discard ginger. Return shredded chicken to pot. Stir in sesame oil and scallion greens. Season with salt/soy sauce to taste.
If soup has cooled, reheat to simmer.
To serve: Divide noodles into bowls. Add broth and chicken. Top with crispy garlic, cilantro, lime wedges, and chili-garlic paste on the side.