Tie peas with kitchen twine in cloth pudding bag or a few layers of cheesecloth, leaving some room for the peas to expand. Place bag of peas, corned beef, onion and pepper in large stock pot or canning pot. Add enough water (about 8 qt/7.5 L) to cover; bring to a boil. Reduce heat to simmer. Cook, covered 2 hr. Next, add potatoes, carrots, parsnips, turnips and cabbage. Bring to a boil again then reduce heat to a simmer. Cook, covered, an additional 20 to 25 min., or until vegetables are tender.
Transfer corned beef to cutting board. Transfer remaining vegetables to large platter, discarding onion (alternatively, cut onion into wedges to serve). Slice corned beef and arrange on top of vegetables. Ladle some of the cooking liquid over top to moisten. Transfer cooked peas from pudding bag into bowl. Stir in butter. Serve alongside Jigg's dinner. Also, set out pickles, pickled beets and mustard as accompaniments.