How to Make It
In a food processor, puree the garlic, paprika, cumin, oregano and 1/3 cup of the vinegar until smooth. Add the remaining 1 cup of vinegar; process until blended.
Heat 1/3 cup of the olive oil in a large enameled cast-iron casserole. Season the pork shoulder with salt and pepper and cook over moderately high heat, turning occasionally, until browned, about 13 minutes. Transfer the pork to a platter.
Add the remaining 2/3 cup of olive oil and heat until shimmering. Season the ribs with salt and pepper and add half of them to the casserole in a single layer. Cook over moderately high heat, turning occasionally, until browned, about 10 minutes. Add them to the pork and brown the remaining ribs. Do not pour off the oil.
Return all of the meat to the casserole and season with salt and pepper. Add the vinegar mixture and enough water to cover the meat and bring to a boil. Simmer over moderate heat until very tender, 45 to 50 minutes. Transfer to a plate and serve.