Husk and rinse the tomatillos, then place them in a blender with the seeded poblano pepper, chopped white onion, garlic, and fresh cilantro.
Add a small splash of the chicken broth to the blender and process until the mixture is a smooth, vibrant green salsa.
Heat the extra virgin olive oil in a medium pot over medium heat, then pour in the blended green salsa and cook for 5 minutes, stirring frequently until the color deepens.
Pour in the remaining chicken broth and add the whole chicken breast, sea salt, and black pepper.
Bring the liquid to a gentle boil, then reduce the heat to low, cover, and simmer for 15 to 20 minutes until the chicken is cooked through.
Remove the chicken from the pot and shred it into bite-sized pieces using two forks, then return the shredded meat to the broth.
Stir in the rinsed hominy and dried oregano, then continue to simmer uncovered for another 10 minutes to allow the flavors to meld.
Ladle the pozole into a bowl and finish with a squeeze of fresh lime juice and a garnish of thinly sliced radishes.