Trim the prime rib and put the best parts aside. Place the bones and fat and the lesser parts into a pot, and cover with water, just enough to cover it all.
Add 1/4 onion, as well as 1 carrot's worth of slices.
Bring to a boil, then reduce and simmer for 2 hours, stirring occasionally.
Pull out and throw away the bones, the meat should fall off, though it may need a little help. Spoon out any good meat and all the carrots.
Pour the remaining stock into a tupperware bowl, through a sifter so the pieces are caught. Throw away these pieces.
Refrigerate the stock for about 2 hours up to a day. Afterwards, spoon off the fat that has risen to the top and discard.
Then pour the stock into a pot. Add meat, sliced celery, potato, remaining carrots, remaining onion, au jus, and thyme. Bring to a boil, then simmer for 2 hours, with the lid ajar, stirring occasionally.
Add barley and simmer for at least 45 more minutes (could be longer), stirring occasionally.
Before serving, remove thyme twigs if you can find them. The herbs will have fallen off by now and will add flavor. Then serve with warm bread or rolls.