1. Dry pork shoulder with a paper towel and make 1” incisions with a knife all over.
2. Pulse garlic, ¼ cup oil, cumin, salt, pepper, and oregano in a food processor until a paste is formed. Remove 2 tablespoons of the paste and set aside.
3. Rub pork shoulder all over with remaining paste, pushing some of it into the incisions.
4. Place pork in slow cooker, cover, and cook on low until meat is fork-tender but not yet completely falling apart, 7 1/2 to 8 hours.
5. To make the sauce, heat remaining ¼ cup oil in a small saucepan over medium heat until shimmering. Add reserved 2 tablespoons garlic paste and let sizzle, stirring continuously until fragrant, just about 1 minute. Remove from heat and let cool before whisking in orange juice, lime juice, serrano, and cilantro.
6. Serve sliced pork over rice with sauce drizzled on top.
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