Preheat the oven to 300ºF.

In a heavy pan or Dutch oven with a lid, just large enough to hold the pork in a single layer, combine the garlic, bbq sauce, hoisin sauce, rice vinegar, soy sauce, broth and salt. Add the pork and turn to coat in the sauce. Cover the pan and cook in the oven for 1 hour.

Remove from the oven and turn the pork. Baste with the pan juices. Return to the oven to cook for another hour.

Turn the pork again and baste with the sauces. Add the ginger. Cover and cook another 1 to 1 1/2 hours, until the pork is falling-apart tender. Baste the meat every 30 minutes.

Remove from the oven and allow to cool enough to handle. Remove the garlic and ginger from the pan and discard. Cut off any visible fat. Use 2 forks to shred the pork in the pan, then mix in with the pan juices.

Fill a large bowl with ice water. Place the lettuce in the ice water to crisp up, making sure the water goes in between each layer.

In a bowl, combine the chili sauce, cucumber, and half of the green onions. Stir to mix. (This will be the dipping sauce.)

To serve, squeeze some lime juice over the pork, then top with the cilantro, peanuts, and remaining green onions. Allow each person to build their own cup with the pork, more lime juice if desired, and the dipping sauce.