Season the lamb shanks on all sides with salt and pepper.
Add the oil to a large rondeau or Dutch oven pot and heat to high until it smokes lightly.
Place in the lamb shanks turn the heat down to medium-high and sear on all sides until they are well browned, which takes about 3 to 4 minutes per side.
Remove the lamb shanks and add the onions and leeks to the pan turn the heat to low-medium and cook while frequently stirring for 25 to 30 minutes or until well browned.
Deglaze with red wine and cook over high heat until it is mostly absorbed into the onions.
Turn the heat down to low medium and mix in the flour until combined to make a roux.
Pour in the beef stock along with the garlic cloves, rosemary sprig, salt, and pepper. Mix to combine.
Place back in the lamb shanks, cover the pot, and cook for 2 ½ to 3 hours over low heat or until they easily fall from the bone.
Remove the Lamb shanks and trim the meat away from the bones.
Roughly cut the lamb into 1” chunks. Set them aside.
Place the trimmed lamb bones back in the pot with the potatoes, carrots, and celeriac root and cook over medium heat until the vegetables are tender, which takes about 30 minutes.
Finish by stirring back in the cut-up lamb shank and parsley, and adjust the seasonings with salt and pepper.
Serve the lamb stew in a bowl with optional garnishes of chopped fresh parsley or rosemary.
Notes
Make-Ahead: You can make this up to 4 to 6 hours ahead. Keep the lamb stew warm over low heat until ready to serve.How to Store: Cover and keep in the refrigerator for up to 5 days. Cover and freeze for up to 3 months. Thaw in the refrigerator for 1 day before reheating. You may also need to add more beef stock and re-season.How to Reheat: Add the desired amount to a small saucepot and heat over low heat until warm. You can substitute the fresh rosemary sprig with 2 teaspoons of dry leaves.If you have a small pot, you may need to sear the lamb in batches. However, it is essential to ensure the lamb can fit back into the pan when braising it.I used an extra-large 12-quart rondeau pan, but a 7-quart plus should work.Other things you can add to the lamb stew are 2 cups of whole button mushrooms 3 peeled, and extra-large diced turnips or parsnips.