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Heat the broiler on high and set rack 6" from heat source. On a foil lined rimmed sheet pan combine the tomatillos, poblanos, jalapeno, garlic cloves and 1 tablespoon of the oil; season with salt and toss to evenly coat. Broil, turning halfway through until nicely charred, about 15 minutes. Transfer poblano chiles to a small bowl and cover with plastioc wrap; let steam for 5 minutes. Peel the peppers and discard skin.
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In a blender, combine the pobanos, tomatillos, jalapeno and garlic and scrape any juices from the sheet pan into the bender. Add the cilantro and puree until smooth.
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Heat oven to 325°.
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In a large Dutch oven, heat the remaining 2 tablespoons oil over medium, Season pork with salt and peppr and add half of it to the pot Cook, turning occasionally, until browned all over, 5 minutes. Transfer to a plate and repeat with the remaining pork.
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After all the pork has been browned and removed from the pot, add the onion and cook, stirring occasionally, until softened, 3 minutes. Add the cumin and oregano and cook, stirring, until fragrant, 1 minute. Return the pork to the pot with any accumulated juices. Add the broth and tomatillo puree and season with salt and pepper. Bring to a boil, cover and tranfer to the oven, Roast until pork is very tender, 1 1/2-2 hours. Season stew with salt and pepper to taste.
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Divide the pork chile verde among shallow bowls, garnish with chopped cilantro and serve warm with rice. Serve lime wedges to be squeezed over the dish.