Place the rotisserie chicken carcass in a large pot. Add the ginger, carrot, celery, onion, garlic, parsley stems, and peppercorns. Pour in enough cold water to fully cover everything in the pot.
Bring to a bubble, then reduce the heat to low, simmering for 2 hours. As it simmers, skim off any foam that rises to the top.
Strain the broth into a large bowl to remove the solids, then return the broth to the pot. At this point, you can keep simmering to reduce the broth for a more concentrated flavour, or move right on to seasoning and finishing.
Remove from the heat, then season with salt to taste, a few dashes of fish sauce, a pinch of sugar, and the lime juice. It should taste super savoury, slightly bright, and perfectly balanced.
Add shredded rotisserie chicken and cooked rice to each bowl, then ladle the hot broth over top. Finish with a bunch of fresh herbs and a lime wedge. Optional: top with sliced chili peppers and/or a little fresh grated ginger.