Pick over the peas and remove any stones.
Wash and drain peas.
Place in a soup pot with the vegetables, herbs, ham hocks and 2 ½ quarts of water.
Bring to a simmer.
Skim the scum off the top of the soup for several minutes, until the scum ceases to rise.
Cover loosely and simmer about 1 ½ hours, or until peas are tender, stirring occasionally in case they stick to the bottom of the pan.
Remove the ham hocks from the soup.
Purée the soup with a blender until desired consistency. An immersion blender works great for this; if you are using a regular blender, take care to work in batches and only fill the blender halfway if the soup is still hot, and hold down the lid while blending. If you want an exceptionally smooth soup, pass the purée through a sieve.
Return the purée to the pot and heat to serve. Add salt and pepper to taste.
Add oil to a non-stick pan on medium high heat. Place diced ham, in batched if necessary, and sauté until ham forms a brown crust. Add back into soup pot and serve.