Heat the oil in a large soup kettle, then cook the onions, carrots and celery for 5 minutes or so, until softened.

Add the ham bone, water and bay leaves.

Simmer for 1-2 hours, then remove the ham bone.

Cut off any tasty looking bits of meat, but realize they will have lost most of their flavor. They'll still add some texture though. I like to keep some ham aside before making the broth and add it when I add the split peas.

Add the split peas (and any other ham you'd like) and simmer another 45 minutes to an hour.

Taste and add salt if needed. Usually the ham broth is salty enough. Remove the bay leaves before serving.

You can use an immersion blender to blend the soup if you'd like a smoother texture or just serve it as is.