This is a very old recipe using simple and cheap ingredients. It's absolutely perfect for a cold winter day.
Before you start, you'll need to soak the dried peas. Overnight is best, but a couple of hours will do. Some packaged peas come with bicarbonate of soda tablets, but if yours don't, add 2 teaspoons yourself. Start the soak with boiling water, and make sure the bicarb is well dissolved.
Peel and chop small the onion, carrot and celery. Melt the butter in a big saucepan on medium heat and stir in the vegetables, whizzing them round to get them all coated in butter. Put a lid on the pan, turn the heat down low and let the veggies sweat for 10 minutes.
Put the ham hock or shank into the pan, and add enough hot water to cover it completely. Add the bayleaf and pepper, and bring to the boil. Turn the heat down, put the lid back on the pan, and cook for 1 hour. Check your peas for doneness - they may take less time or more, depending on the age of the peas and the length of the soak.
Remove the ham and let it cool for a few minutes. When it's cool enough to handle, remove the skin and cut the meat away from the bones. Shred the meat quite finely and add it back to the soup. Depending on the consistency you like, you can either puree the soup to make it smooth, or leave it as it is. You may also add more water to produce a runnier soup, or reduce on high heat to make it thicker.
Whatever you do, your delicious pea and ham soup is now ready. Taste it for seasoning - if it needs salt, add some, but I find that the ham shank adds enough salt.