Place the pozole in a pot and cover with a few inches of water. Stir in 1 tablespoon of salt and half of the onion quarters.
Cover partially and let simmer until the pozole blossoms, about 2 hours.
Remove from heat, drain, and set aside.
Heat a large skillet on medium high heat and roast the remaining onions, garlic, tomatillos and chilies, turning often and allowing to char on all sides, about 20 minutes.
Place the chilies in a plastic bag to steam while they cool. Let the rest of the vegetables cool in a bowl.
If you would like a less spicy pozole, seed the chilies and discard the seeds before adding back to the bowl. If you like a little heat, just remove the stems.
Using a hand blender, puree all of the vegetables together until smooth. If you are having a hard time getting them to blend, simply add a splash of stock.
Heat the olive oil in a large stock pot over medium heat. Add the vegetable puree and salt and let simmer for 10 minutes, stirring occasionally.
Remove from the heat and add the cilantro and epazote, and one cup of broth.
Puree with the hand blender.
Add the remaining broth, pozole, and chicken to the pot.
Return to a simmer for 15 minutes longer, letting the flavors blend and the chicken warm through.
To serve, top with radish slices and wedges of lime.
Tomatillos are a good source of dietary fiber, niacin, potassium and manganese. They are actually more closely related to gooseberries than the commonly associated tomato. They are ripe when their husk pulls away easily. They contain good levels of vitamin C, K, A, and flavonoids such as lutein, and beta carotene. Dietary fiber is especially important for intestinal health as it promotes speedy transition through the digestive tract, eliminating constipation and excess gas. It is also important for regulating blood sugar levels by regulating the release of carbohydrates into the bloodstream.