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1
Dry the pork with paper towels, then season with salt and pepper.
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2
Heat 2 teaspoons of the oil in a 12-inch skillet over med-high heat until just smoking.
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3
Brown half of the pork, about 10 minutes, then add to the slow cooker.
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4
Return the skillet to med-high heat and repeat with 2 more teaspoons oil and the remaining pork.
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5
Add the remaining 2 teaspoons oil to the empty skillet and heat over medium heat until shimmering.
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6
Add the onions, chili powder, and 1/4 teaspoon salt.
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7
Cook until the onions are softened, about 5 minutes.
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8
Stir in the garlic and cook for 15 seconds.
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9
Stir in the tomatoes with their juice, scraping up any browned bits.
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10
Bring to a simmer, then pour into the slow cooker.
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11
Add the broth, hominy, and oregano to the slow cooker.
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12
Cover and cook on LOW for 7-8 hours or on HIGH for 5 -6 hours, until the meat is tender.
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13
Transfer the meat to a large bowl and let cool.
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14
Let the cooking liquid settle for 5 minutes, then use a wide spoon to skim the fat off the surface.
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15
When the meat is cool enough to handle, shred it using your fingers, discarding any gristle; add meat back to cooker.
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16
Before serving, stir in the cilantro and lime juice and season with salt and pepper to taste.