Sprinkle lamb shanks with salt and pepper.

Brown lamb shanks in a Dutch oven or heavy saucepan with oil over medium-high heat.

Remove shanks from the pot and set aside.

Leave only two tablespoons of oil in the Dutch oven.

Add flour to the oil and stir until well combined.

Gradually blend in chicken broth and water, stirring constantly to avoid lumps.

Bring the mixture to a boiling point.

Return the lamb shanks to the Dutch oven along with the sliced onion and chopped garlic.

Reduce heat to low, cover the pot, and simmer.

Cook for 1 1/2 hours, or until the meat is very tender.

Remove the meat from the pot and transfer it to a hot casserole dish.

Add the cut celery pieces to the remaining liquid in the Dutch oven.

Cook uncovered for 10 minutes, until celery is slightly softened.

Add the tomato wedges and minced parsley to the sauce.

Cook for 5 minutes longer, allowing the tomatoes to soften and the parsley to flavor the sauce.

Spoon the sauce and vegetables over the lamb shanks in the casserole dish.

Serve the dish hot with a side of rice or mashed potatoes.