In a large pot add the Ham Shanks or Hocks, add enough water to cover the ham. Add in salt and pepper, oregano, bay leaf, garlic and cut up carrots and onion. Cook for about 2-3 hours on low. Cool until able to handle to the touch.
In a Dutch oven add in the dried split peas, broth and water from Ham. Add salt and pepper. Cook on high to a low boil then turn down to a simmer. Cook the peas for about 1 ½ to 2 hours, till the peas have broken down and the soup has thickened.
While the peas are cooking, sauté the carrots, onions and celery till just about done. Add in the garlic until just aromatic. Add in the carrots, onions, celery and garlic to the soup and continue to cook till the peas have broken down and the soup has thickened.
As the soup simmers, cut meat off of the shank/bone. Add to the soup and simmer for another 15 minutes.
Serve with Croutons or sprinkle with Parmesan cheese and parsley or a good crusty bread.