It is ideal to make this in one pot, preferably one that has a tight fitting lid and can hold everything in it.
Dredge the shanks in the flour and roast them in the oil until golden brown on all sides. Remove from the pan and rest on a plate for a few minutes.
Sauté the onions, celery, and carrots for 10 minutes until slightly caramelized. Add the tomato paste and cook for another 5 minutes, stirring often.
Deglaze the pan with sherry and red wine and bring to a boil. Add all remaining ingredients, including the shanks, back into the pot. There should be enough liquid to completely cover the shanks.
Bring to a boil and transfer to a 300 F oven and braise, covered, for 2 1/2 to 3 hours.
Remove from oven and let shanks set in the braising liquid for a minimum of 2 hours.
Remove the shanks using a slotted spoon and transfer to another tray.
Strain the braising liquid into a saucepan and reduce over medium heat by half until the sauce will coat the back of a wooden spoon. Season the sauce with a little salt and pepper after the reduction is complete to ensure the sauce is not too salty.
Pick all the meat off the shanks and discard the bone. Fill the bottom of a large casserole dish with the picked lamb meat, then cover with enough sauce to moisten the meat but reserving a little for serving later (it should take about 2 cups of sauce).
Top the casserole with the potatoes from the recipe below and add several knobs of butter to the top of the dish just before it goes into the oven. Bake for 45 minutes at 350 F until the potatoes are browned and crispy on top.