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Step 1
Add the annatto seeds (achiote), oregano, coriander, cumin, peppercorns and salt to a food processor or blender. Process to break everything apart. You can also use a mortar and pestle to grind them up.
Step 2
Add the garlic, orange juice, lime juice and vinegar. Process to form a thick paste.
Step 3
Bring the pork shoulder to room temperature. Slice it into 2 inch cubes and set into a bowl.
Step 4
Rub the sliced pork down thoroughly with the achiote paste. Pour in the remaining juices to cover the pork. Cover the bowl and refrigerate. Marinate for at least 4 hours, or overnight for more flavor penetration.
Step 5
Heat your oven to 300 degrees F (150 C). Add the marinated pork with marinade to a large baking dish or pot. Add 1/2 cup water and cover. Bake for 4 hours, or until the meat is fork tender and easily shreds with a fork.
Step 6
Add the marinated pork with marinade to a large pot or Dutch oven. Add 1/2 cup water and cover. Heat to medium-low and simmer for 4 hours, or until the meat is fork tender and easily shreds with a fork.
Step 7
Add the marinated pork with marinade to your slow cooker. Add 1/2 cup water and cover. Cook for 6-8 hours on low heat or 4-5 hours on high heat, or until the meat is fork tender and easily shreds with a fork.
Step 8
Shred the cochinita pibil (cooked pork) with forks. Serve on warmed tortillas topped with pickled red onions, lime wedges, sliced peppers, spicy chili flakes or your own favorite toppings.