Preheat oven to 200°.
Place the beef in a Dutch oven and fill it halfway with water.
Add the crushed garlic, onion, black peppercorns, salt and oregano, and bring to a boil on the stovetop. Once boiling, turn off the heat. Cover tightly, place in the oven and cook for 6 to 8 hours—turning the meat over once during cooking.
When the beef is finished, place it on a cutting board or in a large bowl and, using forks or wooden spoons, pull the meat apart.
Adjust the salt to taste.
Keep the meat warm for making individual tacos. Serve with hot corn tortillas, an array of salsas, coarsely chopped cilantro and Mexican lime wedges.