1. In a 6-8 quart Dutch oven or other heavy pot, heat the olive oil and sugar over medium-high heat, until it starts to turn a very pale tan color.
  2. Add 1.5 teaspoons minced garlic, stirring constantly until the caramel turns a medium brown (20 seconds or so).
  3. Add the pork and brown it on all sides, for 4-5 minutes total, turning often and swirling around the pan to prevent the caramel from pooling and getting too dark.
  4. Add the soy sauce and water, a few grinds of black pepper, the star anise, and the shitake mushrooms. Bring to a boil, then turn down to a simmer.
  5. Braise, covered, for about 1 ½ hours, until the meat is tender and almost falling off the bone. Add the cabbage, and braise for another 20-30 minutes until everything is fork tender. Taste for salt, adding more soy sauce or salt if necessary.
  6. Serve with steamed white rice and garnish with cilantro.