Heat a medium saucepan over high heat until very hot, about 1 minute. Add the chiles and cook, pressing them down with a spatula, until browned in spots, about 1 minute. Add 1 cup chicken broth and bring to a boil. Remove from the heat and set aside.
Heat the vegetable oil in a large pot or Dutch oven over high heat. Add the pork chop bones and cook, turning, until lightly browned on both sides, about 2 minutes. Add the onion, garlic and bay leaf and cook, stirring, until the onion is softened, about 2 minutes. Stir in the oregano and cumin and cook 30 seconds. Add the remaining 3 cups chicken broth and the hominy. Cover and bring to a simmer.
Puree the chile-broth mixture in a blender until smooth; add to the pot. Continue to simmer, uncovered, 10 minutes. Discard the pork bones and bay leaf. Add the diced pork and cook until warmed through, about 5 minutes. Season with salt and pepper. Top each serving with diced onion, sliced radishes and cilantro. Serve with lime wedges.
Photograph by Ryan Dausch