Bring a pot of water to a boil for the pasta. Preheat oven to 325°F.
For the braised pork: In a Dutch oven over medium-high heat, heat 1 tablespoon of oil, about 1 turn of the pan. Sear the pork shoulder on all sides until brown, about 4 to 5 minutes on each side.
Remove to a plate.
Pour a quart of chicken broth into the pot and scrape up all the brown bits with a wooden spoon. Place the pork shoulder back in the pot, put the lid on and put in the oven for 2 hours, until it's tender and falls apart when poked with a fork. Remove from oven, take the pork out of the pot and set it aside until cool enough to handle. Once cool, shred pork with two forks and strain the liquid into a soup pot.