Cut pork shoulder in half; season with salt and pepper on all sides.
Soak shiitake mushrooms in hot water until tender, then remove tough stems if desired. Cut them in half if they are big.
Over high heat, add a bit of oil and sear the meat on all sides. If using an electric pressure cooker, use the sauté function. Transfer to a plate.
Reduce the heat, then sauté the garlic, onions, and mushrooms for about a minute.
Add soy sauce, Shaoxing wine, sugar, and 3 cups of water. If using an electric pressure cooker, add only 1 cup of water.Place star anise and bay leaves in a spice sachet (if available) and add them in. Scrape the browned bits on the bottom and stir to combine. Add the meat and some ground pepper, then let it come to a boil. Cover and simmer over medium-low heat for about 2 hours, until fork-tender; cook on high pressure for about an hour in an electric pressure cooker.
Transfer meat to a plate and remove the spice sachet (or pick out the star anise and bay leaves before serving). Skim the fat layer on the surface.
Make a slurry by dissolving cornstarch in ¼ cup of water. Add the slurry to thicken the sauce.
Add sesame oil, cabbage stalks or white sections, and the meat with the other side facing up. Cook the cabbage for 2 minutes and spoon the sauce over the meat. Add some black pepper.
Slice the meat and pour the sauce over them. Serve with napa cabbage leaves.