Rinse your dried split peas very well. Use cold water and a sieve. Remove any small stones or grit.
Place the ham hock in the large pot. Cover it with fresh, cold water. Bring the water to a boil.
Drain the water and refill the pot. This removes excess salt from the meat. Add the peas to the pot now.
Chop your onion, carrots, and celery. Add them to the pot with the meat. Toss in the bay leaves too.
Bring the soup to a gentle boil. Then, lower the heat to a simmer. Cover the pot with a lid.
Cook the soup for two full hours. The peas should be very soft. The meat should fall off the bone.
Remove the ham hock from the pot. Place it on a clean cutting board. Let it cool for a moment.
Shred the ham into small, bite-sized pieces. Discard the bone and any excess fat. Stir the meat back in.
Check the thickness of your soup. If it is too thick, add water. Season with black pepper to taste.