Soak the peas overnight in water.
Rinse the peas and discard water.
Place a couple of tablespoons of butter in a large heavy-based pot. Over a medium to high heat, soften the onion, carrot, and celery.
After a couple of minutes, add the garlic and continue cooking.
Add about a liter of water, the hock, bay leaves and rinsed peas. Stir and add another liter of water.
Bring to the boil and reduce to a simmer.
Allow to simmer for 4 hours (more liquid may be added if the contents become too dry).
While the soup is cooking, sauté the diced cooked ham in a frying pan over a high heat with a little butter. When it starts to brown, remove from the pan and set aside.
Pour boiling water on the fresh or frozen peas and allow to stand for 1 minute, then strain and set aside.
Once the soup has finished cooking, allow it to cool slightly, remove the hock and bay leaves, and blend or process the soup until smooth.
Return the blended soup to a medium heat and taste for seasoning; it will have been infused by salt from the hock.
Add the cooked ham and peas and serve.