Combine the broth and cilantro stems in a saucepan, cover, and keep warm over a low flame. Season the chicken with salt, pepper, cumin, and oregano. (I didn't measure, but I'd guess about 1/2 a tsp each of the cumin and oregano, maybe a little less of the oregano.) Really rub the seasonings in, and let the chicken sit and come to room temperature if it isn't already.
Heat the oil in a soup pot or dutch oven over high heat. Sear the chicken on both sides (working in batches if necessary), remove to a plate, cover, and set aside until cool enough to handle, then cut into bite-size pieces. (Don't worry if it doesn't cook all the way through--it'll finish cooking in the soup.)
Lower the heat to moderate and add the onion to the pan. Cover and sweat about 3 minutes. Uncover, raise the heat to medium-high, and saute 3-5 minutes, until the onions start to brown and wilt (you're not looking to caramelize them, but they should appear to be on their way). Add the garlic and continue to saute, stirring so it doesn't burn. Add the chipotles and cook, stirring, another minute or two. The aroma filling your kitchen should be pretty awesome at this point.
Strain the broth into the pan with the aromatics and bring to a boil, stirring to scrape up any browned bits, then reduce heat, cover, and simmer a half-hour or so.
Strain the broth once more into a clean pan, pressing on the solids to extract as much liquid as possible. Return to low heat.
For the Assembled Soup:
Warm the fortified chicken broth. Add the corn kernels and the black beans and cook about two minutes, then add the onion, avocado, and chopped chicken (and any accumulated juices) and heat until chicken is cooked through. Remove from heat, stir in the lime juice and cilantro (and radishes, green onions, and/or young garlic greens, if using), and allow to sit for a few minutes. Taste and adjust seasonings. Enjoy.