Sauté the onions, carrots, celery and garlic in olive oil in a pot large enough to hold the shanks, vegetables and broth. Add the shanks, bay leaves, broth and seasonings to taste.
Place a cover on the pot in a tilted position; bring to a boil, then reduce the heat to simmer. Simmer shanks for about 1 to 1 1/2 hours. Check periodically to ensure there is still enough liquid to prevent burning. Adjust seasonings, if necessary.
Remove bay leaves. Once done, the tender, falling-off-the-bone lamb, can be served in individual bowls over a bed of buttered noodles with plenty of vegetables and cooking liquid from the pot. Armenian rice or bulgur pilaf would be an ideal accompaniment in place of the noodles.
Crusty bread or garlic bread (for dipping into the juices) and a tossed green salad make for a very satisfying and traditional lamb shank dinner.