Two of the most iconic preparations, slow-roasted Puerto Rican pernil and Mexican carnitas, are top favorites in their home countries as well as abroad and, of course, in the United States.

Pérnil al caldero is a Puerto Rican staple of succulent slow-cooked pork with shatteringly crisp skin that’s seasoned with adobo, a garlicky, oregano-spiced marinade. The name is a combination ...