Mix the garlic, vinegar, soy sauce, bay leaves, fish sauce, brown sugar, and pepper in a large container or a heavy-duty sealable bag. Add the chicken, turn to coat well with the marinade, and seal the container. Refrigerate from 6 to 24 hours.
Transfer the mixture to a large (as wide as you have it!) deep skillet or a Dutch oven. Add the chicken broth and water. Bring to a boil over high heat, then immediately reduce the heat and simmer, uncovered, until the chicken is cooked and tender and the liquid has evaporated by about ¾, about 1 hour to 1 hour and 10 minutes. After the initial boiling, make sure the liquid stays at a gentle simmer and doesn’t return to a boil. Turn the chicken every 10 to 15 minutes so that it cooks evenly.
When the chicken is cooked through and tender, remove it with tongs (carefully, it should be falling apart tender!) to a plate. Continue simmering the liquid until it has reduced a bit further and has slightly thickened. You should have about 1 1/2 cups of sauce. Return the chicken to the reduced sauce in the pan and turn it to give it a final glazey coating of the sauce.
Place rice on a serving platter, and place the chicken on top of the rice, pouring any extra sauce over the chicken. Serve hot, with the fresh cilantro sprinkled on top, if desired.
Notes
You will want to use a wide-bottomed pan, like a brazier, as you want as much the evaporation of the liquid to be slow but steady. A deep large skillet works well; a large Dutch oven is also a good choice, but avoid deeper stew or soup pots, which won’t allow the liquid to evaporate at the pace it should for everything to get to where it needs to be at the same time. A rondeau is the type of pan used in the Philippines for making adobo, shaped similarly to a brazier.