Heat oven to 250 degrees. Rub pork butt with oil, and season liberally with salt and pepper. In a large Dutch oven over medium-high heat, place meat, fat side down. Brown each side for about 5 minutes.
Remove meat from pot, and pour off most of the remaining fat, reserving enough to saute the celery, onions, and garlic until translucent (about 5 minutes). Add tomato, and deglaze the pot with balsamic vinegar. Pour in beer, and return meat to pot. Bring to a simmer over high heat, and cover. Transfer to oven for 3 hours.
After 3 hours, remove pot from oven, and skim off any excess fat. Add remaining vegetables, and cover. Return to oven for 45 to 60 minutes. When finished cooking, the meat and vegetables should be fork tender.
To serve, slice meat across the grain. Arrange meat slices on platter with vegetables, and sprinkle with parsley.