Preheat oven to 300 degrees. Make the filling: Heat oil in a large Dutch oven over medium-high heat. Season lamb shanks generously with salt and pepper. Working in batches, brown lamb shanks on all sides, about 8 minutes. Transfer lamb to a large plate using kitchen tongs. Reduce heat to medium. Add onion and garlic to Dutch oven, and cook until softened, about 4 minutes. Add tomato paste, and cook for 2 minutes. Add wine, and bring to a boil. Cook for 1 minute.
Return lamb to Dutch oven. Add stock, thyme, and bay leaf. Bring to a simmer. Braise,
covered, for 2 1/2 hours.
Remove Dutch oven from oven, and add celery root and carrots. Braise until meat is falling off the bone and vegetables are tender, about 30 minutes. Let cool slightly.
Meanwhile, make the topping: Peel potatoes, and cut into 1-inch cubes. Transfer to a medium pot, and cover with salted water. Bring to a boil. Reduce heat to low, and simmer until tender, about 20 minutes. Drain, and pass potatoes through a ricer. Return potatoes to pot, and add cream, butter, and 2 teaspoons salt. Cook over medium heat, stirring until combined and warmed through. (If not assembling potpies immediately, place a piece of plastic wrap directly on the surface of potatoes to prevent a skin from forming.)
Transfer lamb to a plate using a slotted spoon, and remove meat from bones. Break into smaller pieces using a fork. Skim fat from remaining cooking liquid. Return lamb to Dutch oven, and stir.
Heat broiler. Transfer filling to a 12-inch (8-cup) gratin dish using a slotted spoon. Add 1/4 cup cooking liquid. Spread mashed potatoes over top, covering the entire surface. Broil 5 inches from heat source until potatoes are golden brown, about 5 minutes. Serve remaining cooking liquid on the side.
Mashed potatoes can be refrigerated for up to 3 days; reheat before using.
Perfect for an autumn dinner party. Total do ahead. I browned the shanks in a large skillet instead because I increased the size of the recipe. I mixed the braising liquid the skillet, then braised in a large roasting pan covered tightly with foil. I then pulled away the meat, chilled it, and removed fat. I had made the potatoes ahead and assembled the pie in the gratin dish the afternoon of the party. I warmed the dish, and then added Parmesan cheese and ran it under the broiler. Yum!