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1
In a large enameled cast-iron casserole, heat 2 tablespoons of the olive oil.
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2
Season the pork with salt and pepper, add to the casserole and cook over moderately high heat, stirring twice, until browned, about 8 minutes.
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3
Add 1 piece of the quartered onion, the cloves, the 1 tablespoon of oregano, the bay leaves and 6 cups of the beef broth and bring to a boil.
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4
Cover and simmer over moderately low heat until the pork is tender, about 40 minutes.
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5
Discard the bay leaves.
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6
Meanwhile, heat a large cast-iron skillet.
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7
In a large bowl, toss the tomatillos, tomatoes, garlic and remaining 3 pieces of onion with 1 tablespoon of the olive oil; season with salt and pepper.
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8
Add the vegetables to the skillet and cook over moderately high heat until blistered in spots, about 10 minutes.
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9
Transfer the vegetables to a blender.
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10
In the same skillet, toast the chiles over moderately high heat until slightly darkened, about 2 minutes.
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11
Add the remaining 2 cups of beef broth and bring to a simmer; cover the skillet, remove from the heat and let the chiles soften for 5 minutes.
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12
Add the chiles and broth to the blender with the vegetables and puree until smooth.
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13
Strain the vegetable-chile puree into a bowl.
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14
Wipe out the skillet.
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15
Heat the remaining 1 tablespoon of olive oil in the skillet.
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16
Add the chorizo and cook over moderate heat, breaking it up with a spoon, until browned, about 5 minutes.
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17
Add the chorizo, hominy and vegetable-chile puree to the casserole and bring the pozole to a simmer.
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18
Season with salt and pepper.
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19
Garnish the pozole with radishes, onion, cilantro and oregano and serve with lime wedges.
