In a large pot over low-medium heat, melt the butter and add the orzo. Stir frequently, letting the orzo turn golden and toasty for a few minutes. Be careful not to burn the butter or orzo. Remove the orzo from the pot and set aside.
In the same pot, add a drizzle of olive oil over medium heat. Sauté the chopped onion, celery, and garlic until softened, about 3-4 minutes. Season with salt and pepper.
Pour in the chicken stock and 3 cups water. Bring to a simmer, then add the chicken breasts or thighs. Cook the chicken in the broth until fully cooked through (breasts will take less time than thighs), about 10-15 minutes.
While the chicken is cooking, combine chili flakes, sesame seeds, garlic, ginger, sugar, salt, and a cinnamon stick in a heat-safe bowl. Heat the neutral oil in a small pan until hot (test by adding a small piece of garlic—if it sizzles, it's ready). Carefully pour the hot oil over the chili mixture and stir. Set aside to infuse.
Once the chicken is cooked through, remove it from the pot and shred it with two forks.
Add the toasted orzo back to the pot of broth. Stir occasionally over medium heat until the orzo is tender, about 7-8 minutes.
Return the shredded chicken to the pot and stir in the lemon juice. Adjust seasoning with salt and pepper as needed.
Ladle the soup into bowls and top with a drizzle of Aunt Lily’s Chili Oil, fresh chives, and extra lemon juice if desired.