Remove the meat. Strain the cooking liquid into a large bowl, and then add the liquid back to the pot. (You can save the remaining broth to make a soup or stew later.)
Add the meat and sauce ingredients to the pot. Bring it to a boil over high heat. Reduce the heat to medium, and boil, covered, until the meat is tender and the sauce is reduced. You can cook longer if the meat is still not tender enough.
Add the optional dried kelp, peppers and eggs and continue to boil. Discard the kelp, and transfer everything else to an airtight container for storage. Shred the meat and pour some sauce over to serve.