1. Cook, drain, and rinse the hominy. Set aside.
2. Husk and halve the tomatillos. Peel and quarter the onion. Core, deseed, and quarter the chiles.
3. Chop the cilantro coarsely and set some aside for garnish. Peel garlic.
4. In a food processor, combine halved tomatillos, quartered onion, poblanos and jalapeños, garlic, and chopped cilantro.
5. Blend until smooth, adding a bit of water if necessary and scraping down the sides of the bowl to incorporate all the bits.
6. In a large soup pot, heat olive oil, 2/3 of the tomatillo puree, sea salt, coriander, and cumin.
7. Cook over moderate heat, stirring occasionally, until the sauce turns a deep green, about 10 minutes.
8. While this is cooking, add one quarter hominy to the blender with the reserved tomatillo mixture, and blend until smooth.
9. Shred the cooked chicken if not done already.
10. Add the chicken broth, shredded chicken, and the remaining three quarters of the the hominy.
11. Bring to a simmer over moderate heat and cook until just heated through.
12. Right before serving add the reserved tomatillo/hominy mixture into the soup. Season with additional sea salt, and fresh ground pepper to taste.
13. Peel, pit and slice the avocado. Slice the radishes thinly and slice the lime into wedges.
14. Garnish each bowl with avocado, radishes, reserved cilantro, and optional queso fresco. Serve with a wedge of lime.