Char the poblanos. Toast the poblanos over an open flame until they’re blackened all over. Alternately, place them on a baking sheet and toast them under the broiler until they’re charred all over. Place the peppers in a heat-proof bowl and cover tightly with plastic wrap. Once the peppers are cool enough to handle, peel off all the skin and roughly chop them.
Clean the tomatillos. Remove the husks from the tomatillos and rinse them under cold water until the outsides are no longer sticky. Cut the tomatillos into wedges.
Sear the pork. In a 5-6 qt dutch oven, heat the oil over medium-high heat. Pat the pork pieces dry, season them all over with salt and pepper and sear in batches until browned all over. Transfer the pork to a plate.
Build the sauce. Add the onion, chopped tomatillos, and serranos and saute them in the hot oil until they’re softened, about 4-5 minutes. Add the chopped roasted poblanos, garlic, cumin, and oregano and cook for another 2 minutes. Add the contents to a blender with the chicken stock and half of the cilantro and blend until very smooth.
Simmer the chile verde. Pour the salsa verde back into the pot and season it with salt and pepper. Bring the sauce to a simmer, using a wooden spoon to scrape up any browned bits off the bottom of the pot. Add in the pork (along with any juices), cover and simmer on low heat for 2 ½-3 hours, until the pork is tender. Stir in the rest of the cilantro and the lime juice and season to taste with salt and pepper if needed.
Serve. Ladle the pork into bowls over rice and top with sliced radish, cilantro, diced white onion, and more lime.