Combine stock, bay leaves, onion quarters, garlic cloves, peppercorns, and salt in a large pot.
Bring to a simmer, cover loosely, and cook 30 minutes.
Strain the broth into a bowl; discard solids.
In the same pot, heat oil over medium. Add diced onion and jalapeño; sauté 3–4 min until translucent.
Push vegetables to one side. Sprinkle in masa harina and toast in the oil 3–4 min, stirring constantly, until light golden and smelling like toasted corn.
Add minced garlic, cumin, oregano, allspice, and lime zest; stir 15 sec to bloom.
Add tomatoes and cook until they darken and reduce (3–4 min).
Gradually whisk in a ladle of the hot broth to smooth the roux, then pour in the rest while stirring. Bring to a gentle simmer.
Add the whole chicken breasts to the simmering broth.
Maintain a gentle simmer (~190–195 °F) for 15–20 min, until internal temp hits 160 °F.
Remove breasts, let rest 5 min, then shred and return to the pot.
Stir in cooked rice (if using) and simmer another 5 min.
Taste and adjust salt.
Off heat, add lime juice and cilantro.
Ladle into bowls and top with crispy tortilla strips, avocado, cotija, radish, and a final lime squeeze.