Melt the butter in a soup pot and then add the carrots. After the carrots have cooked for a little bit stir in the onions and celery. When the onions have turned translucent add the chicken stock. Heat the braising liquid until it reaches a light boil. Add enough chicken stock so that the 1/4 of the pork is submerged. Put the lid on upside down, or cover with tin foil so that there is a concavity so that the rising moisture will collect and drip on the pork shoulder. Sear the pork for 35 minutes in a pre-heated 400 degree oven. Turn the heat down to 300 degrees and cook for 1 hour or until the internal temperature has reached 155 degrees.