Heat the oil in a Dutch oven over medium heat. Dry the pieces of meat with a towel, season them well with salt and pepper, and brown them on all sides; set them aside. Add all but 1 teaspoon of the garlic and all of the shallots to the pan; cook until golden, about 6 minutes. Splash in the wine; simmer 5 minutes. Add the stock, orange juice, lemon juice, tomato paste, rosemary, the reserved lamb shanks, and any juices they have released. Cover; simmer gently for 45 minutes.

Stir in the orange and lemon zest, parsnips, rutabaga, and celery root. Cook until both the lamb and vegetables are tender, about 20 minutes more, partially covered. Set aside to cool. When the lamb is cool enough to handle, remove the meat from the bones and add it back to the stewed vegetables. Discard the bones.

Bring a large pot of salted water to a boil. Cook the pasta until al dente. While the pasta is cooking, combine the remaining teaspoon of garlic with a few drops of olive oil in a large skillet or pot over high heat; cook a few seconds until fragrant, then add the lamb and vegetable stew; bring to a simmer. Using a slotted spoon, transfer the cooked pasta directly from its cooking pot to the skillet with the stew. Add the butter, cheese, and parsley; toss to combine. Season well with salt and pepper, and serve in heated bowls, garnished with lemon wedges.