Heat oil in a heavy casserole dish.

Brown lamb shanks on all sides. Remove from the casserole dish.

Add chopped carrot, celery, onion, and cubed turnip to the casserole dish.

Cook the vegetables, stirring to glaze them in the rendered fat.

Return the browned lamb shanks to the casserole dish.

Add salt, pepper, thyme, and chicken broth (or water).

Cover the casserole dish and cook until the lamb is tender, approximately 1 hour.

Add rice to the casserole dish, ensuring the lamb shanks are raised slightly so the rice is submerged in the liquid.

Add more broth if necessary to cover the rice by about 1 inch.

Add green beans and quartered tomatoes to the casserole dish.

Cover the pan tightly.

Bring the mixture to a boil, then reduce heat to a simmer.

Simmer for about 20 minutes, stirring once, until the rice is cooked and the lamb is very tender.

Serve hot.