Thinly slice the vegetables and place in a large stainless steel or glass bowl.
Pour the vinegar and sugar into the bowl, add a pinch of salt, and stir to combine.
Add the vegetables to the pickling liquid, cover, and refrigerate for at least 1 day, stirring once a day.
Preheat oven to 325°F.
Salt the pork liberally and brown it on all sides in an oven-safe pot.
Add the garlic, cumin, oregano, chili flakes (if using), pepper, and enough water to come halfway up the meat.
Cover the pot and braise in the oven for 3-3.5 hours, flipping the meat and replenishing the water as needed.
Remove the meat from the pot and let it cool.
Skim the rendered fat from the braising liquid and boil it down to a thick glaze.
Pull the meat off the bone in chunks and add it to the glaze, shredding it with two forks.
Taste the pork and add salt if needed.
Serve the pork with the pickled vegetables, garnished with cilantro leaves and some of the pickle juice.
