Trim off and discard skin from ham hocks.

In a large soup pot or Dutch oven, melt butter over medium heat. Add carrots, celery and onion. Cook, stirring regularly, until softened, about 10 minutes.

Stir in dried split peas, bay leaf ,savory and thyme. Cook, stirring, for about 2 minutes.

Stir in chicken broth and water. Add the ham hock. Bring to a boil, then reduce heat to medium-low, cover the pot and simmer, stirring occasionally, until the peas are very soft and soup is thickened, about 1 ½ - 2 hours. *NOTE: You may need to add additional water or stock if soup gets too thick.

PICK OUT AND DISCARD BAY LEAF and remove the ham hock to a plate. *Note: I prefer a thicker soup, so I blend just a bit of the soup with an immersion blender or blender. Just do a quick blend (or blend just a cup of the soup. You don't want a completely pureed soup. You want it to retain most of it's texture, but the bit of pureed soup will incorporate with the broth for a thicker soup.)

Let ham hock cool slightly, then remove any meat on the hock and add it back to soup. Discard the fat and bone from the hock.

Stir to combine meat with soup. Taste and generously season with salt and pepper, to taste.