Put the skinless thighs, broth, onion halves, garlic, oregano, cumin and salt in a large pot. Bring to a bare simmer and skim any foam in the first 10 minutes.
Simmer gently, partly covered, 25 minutes. A hard boil clouds the broth and toughens the meat; lazy bubbles are the setting.
Add the carrots, potato and corn rounds. Simmer 15 minutes.
Add the zucchini and simmer 8 to 10 more minutes, until every vegetable is tender but intact.
Pull the thighs, shred the meat off the bones in big pieces, and return it to the pot. Discard the bones and onion halves.
Taste for salt boldly; a big brothy pot hides underseasoning. Serve in deep bowls with cilantro, lime wedges and warm tortillas.