In a large pot set over medium-high heat, bring the chicken stock to a boil. Add the chicken pieces, tomatillos, onion, poblanos and jalapenos, oregano, and salt. Return to a boil, then reduce the heat to low, cover and simmer for 40 minutes until tender.
Carefully remove chicken from pot and shred the meat, discarding any bones and skin. Skim fat from the cooking liquid and reserve.
Place a large fine mesh strainer over a large bowl and strain the broth through it. You could also use a spaghetti strainer and pour into a bigger pot. Set aside.
Transfer the solids to a blender. Add garlic cloves, cilantro, and 1 cup of the broth and puree until it reaches your desired smoothness. Season with salt and pepper to taste.
Return Dutch oven to stovetop, setting it over high heat. Add 2 tablespoons of the skimmed fat to the pot and allow to cook and sizzle for 30 seconds.
Pour the tomatillo puree to the pot and stir, being careful not to get splattered with the hot sauce. Reduce heat to medium. Add the stock and stir to combine, then stir in the shredded chicken and drained hominy. Cook for 10 minutes until warmed through, seasoning with salt and pepper as desired.
Serve the pozole garnished with cilantro, sliced radishes and jalapeno, avocado, and lime wedges.