Step 1

In a large Dutch oven over medium, heat the oil until shimmering. Add the onions and 1/4 teaspoon salt and cook, stirring, until beginning to brown, about 5 minutes. Add the chilies, garlic, coriander, cardamom, cilantro stems and half of the tomatoes. Cook, stirring constantly, until fragrant, about 30 seconds.

Step 2

Add the broth and bring to a simmer over high. Submerge the chicken breasts, cover and cook over low until the chicken registers 160°F and is no longer pink at the thickest part, about 30 minutes.

Step 3

Transfer the chicken to a large plate and set aside to cool. Use a mesh strainer to strain the broth into a large heatproof bowl, discarding the solids, then return the broth to the pot. When the chicken is cool enough to handle, shred the meat into bite-size pieces, discarding the skin and bones.

Step 4

Add the chicken to the broth and bring to a simmer over medium-high. Remove from the heat and stir in the remaining tomatoes, the cilantro leaves and lime juice. Taste and season with salt and pepper. Serve with lime wedges, radishes or cabbage (if using), and hot sauce.