Drizzle beef shoulder with oil, then season with plenty of salt and black pepper. Set a large, heavy-based pot over medium-high heat. Sear on all sides until you have a nice brown crust, adding additional oil to the pan as necessary to prevent sticking. Add onion and garlic to the pot and stir until they caramelize a little and have contact with the bottom of the pot. Add tomatoes with juice, chiles, cumin, chile powder, and the 1/2 bunch cilantro. Add 2 inches of water to the pot. Crush tomatoes with the back of a wooden spoon. Cover and simmer about 2 hours, until the meat is fork-tender and comes apart with little resistance. Once cooked, use a wooden spoon to break apart the meat. Season with salt and black pepper to taste; add the vinegar.

If you like, warm the tortillas over an open flame on a gas stove, about 10 seconds per side. Serve the meat in tortillas with romaine, cilantro, cheese, and lime wedges.