Boil the pot barley in unsalted water for 25 minutes, then drain it.
Preheat an oven to 160C/320F/Gas 3.
Peel the onions and slice them into thick rings.
Cut the celery into short lengths.
Peel the parsnip, carrot and potatoes and cut them into fat chunks.
Pile the vegetables into a large deep pot, then tuck in the chops, thyme and bay leaves.
Add the corned beef.
Season with a little white pepper, no salt, then pour in the drained barley and enough water or stock to cover the meat and vegetables completely. Bring it slowly to the boil.
Skim off the froth that accumulates on the surface with a slotted spoon.
Cover the top of the stew with a sheet of greaseproof paper, then with a lid. Transfer the pot to the oven and cook for two hours.
Remove the lid. The liquor should be thin, thickened only slightly by the potatoes. Chop the parsley and mix it in carefully, so as not to smash the vegetables, then season with salt and freshly ground black pepper.
Leave overnight. Next day, skim the fat from the top, then reheat slowly on the stove until the meat is thoroughly hot and the broth gently bubbling. Season as required and serve piping hot.