In a large bowl, combine the garlic, olive oil, orange juice, lime juice, ground cumin, dried oregano, salt, and black pepper to create the marinade.

Place the pork shoulder in a resealable plastic bag or deep dish and pour the marinade over it, ensuring it's evenly coated. Refrigerate for at least 4 hours or overnight.

Preheat your oven to 325°F (165°C). Prepare a roasting pan by lightly greasing it.

Remove the pork from the refrigerator and let it come to room temperature for about 30 minutes. Roast in the prepared pan for 3 to 4 hours, basting occasionally until the internal temperature reaches 190°F (88°C).

Let the pork rest for 15 minutes before slicing or shredding. Serve with rice, black beans, and fried plantains.