Place all the ingredients except for the water in a Dutch oven or any heavy-duty pot and let them marinate for about 30 minutes.
Place the pot over medium heat, add 1/2 cup of water, and bring it to a boil. Lower the heat to a simmer and cook without stirring until most of the vinegar's acidity has cooked off. You'll know it's done when the smell is no longer sharp or "stingy."
Continue simmering over low heat until the chicken is very tender, about 40 minutes to an hour. Taste the sauce; if it's too salty or sharp for your liking, add some of the remaining water. I usually use a total of 3/4 cup.
When the chicken is tender, remove the pieces from the pot and set them aside. The garlic will also be very tender at this point; you can mash some (but not all) of the cloves against the sides of the pot to incorporate them into the sauce.
Continue simmering on low heat for an additional 30 minutes to 1 hour, or until the pork is meltingly tender. Once the pork is very tender, remove it from the pot and set it aside. Keep simmering the sauce until it reduces to your desired consistency. Taste the sauce; if you'd like a bit of sweetness, stir in a pinch of brown sugar. I like to do this, but it’s not necessary.
Heat a skillet with some oil over high heat. Once the oil is hot, add the chicken and pork pieces and fry them until browned.
When the sauce has reduced to your desired consistency, add the browned chicken and pork back to the pot. Toss gently and remove from heat. You can eat it at this point, but the dish gains depth of flavor if you let it rest for a day.