Place the whole chicken in a pot large enough to cover it completely with water by about 2 inches. Place the pot over high heat and bring the water to just below a simmer. Reduce the heat and cook the chicken for approximately 2 to 3 hours. Skim any white foam that develops on the surface of the water. It's flavorless, but this scum will turn your broth a grey-ish color if you don't remove it.
When done, the meat should fall off of the bone, but it shouldn't be mushy. Transfer the chicken to a pan and let it cool down a bit. Reserve the broth.
Pull all of the meat from the chicken bones and discard the carcass. Break down any larger pieces of meat so everything is somewhat consistent in size. Reserve the chicken meat for later on in the recipe.
Grab a cast iron pan (if you don't have cast iron a fry pan will do) and place it over medium-high heat. When it's hot, add the peppers, tomatillos, a peeled and quartered yellow onion, and the garlic cloves with their skin on. The skins will protect the garlic from burning in the pan while roasting.
Roast the vegetables on the stove top until they've browned slightly. Turn the vegetables often so they cook evenly. It's not important to cook the vegetables through on this step. Just brown them lightly, then transfer the veggies to a pan to cool off.
Clean the peppers by removing their seeds and stem. Peel the garlic, then place all the vegetables in a blender along with the cilantro. Process the mixture on medium-high speed until pureed, then add it to the pot with the chicken broth.
Bring the liquids to a simmer and cook them for 20 to 30 minutes. Stir in the hominy as well as the oregano and cumin and simmer the pozole for an additional 15 minutes.
Now, add the chicken and adjust the seasoning with sea salt if necessary.
Thinly slice some radish and green cabbage. Pick fresh cilantro leaves and dice a few semi-ripe avocados.
Ladle portions of the pozole into soup bowls and top with the shaved vegetables, cilantro and avocado. For a little crunch, you could also add some crumbled tortilla chips.