Combine pork shoulder with adobo (pineapple quarters soaked in a mixture of spices), onions, cilantro leaves. Marinade for at least 2 hours or overnight to allow flavors to penetrate the meat.
Preheat grill or stovetop skillet to high heat. Grill marinated pork until fully cooked and slightly charred on all sides, about 5-7 minutes per side depending on your preferred level of doneness. Alternatively, you may use a slow cooker if desired.
Allow the meat to rest for several minutes before slicing against the grain into thin strips. Serve immediately with warmed tortillas and top with additional lime wedges.