Heat the oil in a heavy pot over medium-high. Brown the pork in two batches until the pieces have color on a couple of sides, about 3 minutes per batch. Set aside.
Drop the heat to medium, add the garlic, and cook for about a minute until fragrant and just starting to color.
Return the pork with the vinegar, soy sauce, water, bay leaves, peppercorns, and sugar. Bring it to a simmer and do not stir for the first 5 minutes. This is the old adobo rule, and it is real: stirring early keeps the vinegar tasting raw and sharp.
Cover and keep it at the gentlest possible simmer for 30 minutes, until the pork is tender. A rolling boil will wring a lean cut dry, so check the heat once or twice.
Uncover, raise the heat, and reduce the sauce for 8 to 10 minutes, turning the pork in it, until it is glossy and just coats the meat.
Rest 5 minutes and serve over rice with plenty of the sauce.