Chop carrot, celery, onion, and garlic, then add to a 6-quart Dutch oven.

Add olive oil, and sauté until the vegetables are tender. Pick through the split peas, discarding any foreign matter, then wash thoroughly in a strainer. Add to the Dutch oven, along with the thyme, and bay leaves.

Next, add the ham bone, ham broth, water, and pepper. If you don't have any ham broth on hand, you can use chicken or vegetable broth instead.

Bring the soup to a boil, then simmer, covered, for approximately one and a half hours. Ham tends to be very salty, which is why I omit salt from this recipe.

After the soup has cooked long enough, remove the ham bone, and allow it to cool. Trim all the ham off the bone, and add to the soup. If you like the soup pureed, do so before adding the ham.

Lastly, stir the milk in, if using. The milk makes the soup taste less salty and creamier. This soup is ham bone as is, or with crackers.