Season the lamb shanks with salt and pepper, to taste. Heat the oil in large heavy pot over medium-high heat. Working in batches, if necessary, to not overcrowd the pan, sear the shanks on all sides until deep brown, about 7 minutes. Remove the shanks to a plate and add the port. Bring to a simmer, scraping any brown bits off bottom of pan and reduce by 1/3. Add the mulling spices, wrapped in cheesecloth or in a muslin tea bag. Return shanks to the pot, adding water if needed, to cover the meat. Cover and simmer until the meat is tender, about 2 1/2 hours. Remove the shanks to a cutting board and let rest. Discard the mulling spices. Simmer the braising liquid until reduced and thickened, about 20 minutes.
Meanwhile, cook the pasta to al dente according to package directions in a large pot of salted boiling water, about 4 minutes. Pull the meat from the bones, chop it and add it to the sauce. Drain the pasta, and add it to the meat and sauce. Toss and serve immediately. Enjoy!