Preheat the oven to 350 degrees.
Place the 1/3 cup of the flour on a large plate and season liberally with salt and pepper. Dredge the lamb shanks in the seasoned flour, coating them on all sides.
In a large ovenproof pot or Dutch oven, heat 1 tablespoon of the oil over moderately high heat. Cook the shanks on all sides until brown, about 5 minutes. Remove the shanks to the side.
If the oil in the pot looks burnt at all, remove with a paper towel. Add the remaining tablespoon of oil to the pot and place over low heat. Add the leeks, garlic and onions and cook, stirring, for 5 minutes. Add the parsnips, carrots and half the parsley, the rosemary and thyme and cook for 2 minutes. Raise the heat to moderately high and sprinkle in the remaining 1 1/2 tablespoons flour. Stir to coat all the vegetables. Add the wine and bring to a boil. Add the stock and simmer. Reduce heat to low and tuck the shanks into the broth and vegetables. Remove from the heat and cover the pot.
Bake on the middle shelf for about 1 1/2 to 2 hours, or until the lamb meat is practically falling off the bone and is very tender. Remove from the oven, sprinkle with the remaining parsley and taste for seasoning.
If not serving right away, cover and refrigerate overnight. The next day, remove almost all of the fat that has formed on top of the stew (but do leave a little for flavor). Reheat in a low 275-degree oven or over medium heat until hot and bubbling. Season to taste.
To make the gremolata: Mix all the ingredients in a small bowl. The gremolata can be made a day ahead of time; cover and refrigerate.
To serve: Spoon out the lamb and vegetables and juices from the pot and top with a sprinkling of gremolata.

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