Place the salt beef in a large pot and cover with cold water. Let it soak for 2-6 hours, changing the water every hour to reduce the saltiness. If you don't have time to soak it, boil it once and then discard the water, and continue with fresh water.
After soaking, drain the water. Place the beef in a large pot and cover with fresh cold water. Bring to a boil, then reduce heat and simmer for about 2 hours.
About 45 minutes before the beef is done, add the turnips and carrots to the pot.
To make the pea pudding, combine the split peas, salt, pepper, and lard/butter in a bowl. Place the mixture in a muslin or cloth bag and tie it tightly. Place the bag in the pot with the beef and vegetables.
About 20 minutes before the end, add the potatoes and cabbage quarters to the pot.
Continue to boil until all vegetables are tender.
Carefully remove the pea pudding bag, vegetables, and beef from the pot. Place them on a large platter or in separate serving dishes.
Cut the beef into thick slices. Open the pea pudding bag and transfer the contents to a bowl, mashing it slightly.
Serve the salt beef with the boiled vegetables and pea pudding. Enjoy!