Wrap the onion and ginger in a large piece of foil. Place directly over open flame on a gas stove and cook for 15 minutes until soft and charred. Turn over at half-way mark. Remove from flame. Once cool, peel both the onion and ginger removing any charred layers. With the onion, trim off the root end then cut into it halfway, as if cutting it in half but still leaving it in tact. Bruise the ginger with the broad side of a cleaver or chef’s knife. Set both aside.
While cooking the onion and ginger (step 1), toast all the spices (last 5 ingredient items) in a dry pan for 2-3 minutes to release their fragrance and heighten their aroma in the broth. Allow to cool, then wrap in double layer of cheesecloth and tie securely.
Heat oil in large soup kettle, stock pot or dutch oven. When oil shimmers and just begins to smoke, add the chicken breast pieces; brown on both sides, about 5 minutes total. Remove and set aside.
Add the remaining chicken pieces to the pot; sauté until no longer pink, 4 to 5 minutes. (Do this in batches if it does not all fit into the pot without overcrowding). Reduce heat to low, cover, and simmer until chicken releases its juices, about 20 minutes.
Increase heat to high; add 3-4 quarts water along with the breast pieces, rock sugar salt, fish sauce, and cheesecloth pouch of spices. Return to simmer, then cover and barely simmer until chicken breasts are cooked and broth is rich and flavorful, about 20 minutes.
Remove all chicken pieces from broth; set aside. When cool enough to handle, remove skin, then remove meat from bones and shred into bite-size pieces; discard skin and bones.
Using a fine mesh sieve, strain broth; discard onion, ginger, and spice pouch. Add more salt and fish sauce to the broth according to your taste.