Add chicken broth, water, dried split peas, ham bone or ham hock and bay leaf to a large pot. Bring to a boil then lower heat and simmer for one hour.
Remove ham bone. At this point, I usually add another cup of water since the peas absorb a lot of the liquid.
Use a hand-held blender to create a smooth texture.
Add the onions, celery, carrots, potatoes and ham. Also add the Worcestershire sauce, parsley, basil, Italian seasoning and horseradish.
Bring to a boil then lower heat and simmer for one hour or until vegetables are cooked through.