Heat oil in a large pot over medium heat. Saute the garlic, shallots and Serrano chiles until soft and fragrant (about 8 minutes).
While garlic mixture is cooking, puree tomatillos in a blender until smooth.
Add half of the tomatillo puree to the pot and saute until thickened (about 5 minutes). Season with salt and pepper.
Add 2 c chicken stock and hominy to pot and bring to a simmer. Cook for an additional 10 minutes.
Meanwhile, combine 1 c cilantro with remaining tomatillo and blend until smooth.
Add the shredded chicken, lime juice and cilantro-tomatillo puree to the pot, remove from heat and stir to combine. Season to taste with salt and pepper.
Divide posole among four bowls and garnish with radish, cabbage, avocado and cilantro to serve. Lime wedges optional.