In a pot, boil about six cups of water. Add salt. Throw in the garlic, onion, peppercorns, bay leaf, celery stalk and carrot. Boil for five minutes then add the meat pieces. Stir. Boil for 10 to 15 minutes. Scoop out the meat, spread on a tray and cool.
Heat the butter or vegetable oil in a frying pan. Brown the pork in batches until lightly browned. Add more oil with each batch if the pork does not render enough fat.
Return all the pork in the pan.
Reserve about half a teaspoonful each of the orange and lime zest. Add the rest to the pork. Pour in the lime and orange juices, and honey. Sprinkle with a bit more salt, if needed. Stir. Cover the pan and cook over very low heat for about 10 minutes or just until the liquids have turned syrupy.
Turn up the heat to medium-high and cook the meat for another few minutes until the sauce is thick and coats each piece of pork generously.
Arrange the pork on plates (or a single platter). Drizzle the syrupy sauce over them. Sprinkle the reserved zests on the meat (and some snipped greens, of you have any).
Serve the orange lime honey pork with rice or by itself.