Preheat oven to 325˚F (160°C). In bowl, mix together the broth, beer (or water), hoisin sauce, ketchup, soy sauce, rice vinegar, brown sugar, hot chili sauce and onion. Set aside.
Place oil in Dutch oven set over medium-high heat. Brown beef on all sides. Pour broth mixture over beef. Cover and braise in oven 3 hr., or until meat is very tender. Transfer beef to large bowl. Skim fat from sauce in Dutch oven.
After beef is cool enough to handle, pull into shreds with two forks or with your hands protected with kitchen gloves. Place Dutch oven on stove and bring sauce to a simmer; mix in shredded beef.
Spoon beef into serving bowl. Also set out bowls of lettuce leaves, carrot, cucumber and cilantro (or green onion). Let diners fill lettuce leaves with meat and vegetables.
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