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1
Roast green chiles: place peppers, skin side up, in a single layer on a baking sheet lined with foil. Place baking sheet on top rack in oven and broil on high until peppers are blackened and blistering, about 10-12 minutes.
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2
Immediately transfer peppers to a medium bowl and cover tightly with plastic wrap. Let tomatoes and peppers sit inside the bowl for 5-10 minutes (this steams them, which will make the skins much easier to remove).
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3
Peel charred skins off of peppers, discard skins. Chop peppers into thin strips and set aside.
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4
While peppers are roasting/steaming, blend tomatillos and chicken broth using a food processor or blender until a smooth consistency is achieved. Set tomatillo mixture aside.
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5
In a large bowl, toss the chopped pork shoulder with the flour, 1 tsp salt, and 1/2 tsp pepper, until pork pieces are evenly coated.
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6
Heat 2 tsp of the oil or bacon fat in a large pot or dutch oven over medium heat, and once hot, add half of the pork pieces in a single layer. Cook, 1-2 minutes per side, until pork is browned on all sides. Remove pork from pot and place on a paper-towel lined plate.
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7
Heat another 2 tsp of the oil or bacon fat in the pot and repeat step 6 with the remaining pork pieces. Once browned, transfer to plate as well.
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8
Add the final 2 tsp of oil or bacon fat to the pot, add the onion, garlic, cumin, chile powder, 1/2 tsp salt, and cayenne pepper. Cook until onions are soft and translucent, about 3-4 minutes.
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9
Add the chopped roasted green chiles, and cook 1 additional minute.
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10
Add the tomatillo mixture, tomato paste, lime juice, pork and 1 cup water. Stir to combine.
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11
Bring to a boil, then reduce heat to low, and simmer, covered, for 2 hours, stirring occasionally.
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12
After 2 hours, pork should be very tender and shreddable. Break pork apart with a large fork, and stir. Season to taste with salt. You can serve as is, or continue to cook, uncovered, for an additional 10 minutes for a thicker consistency if desired. Ladle into bowls and serve with fresh cilantro, warm tortillas, lime wedges and hot sauce.
