Preheat oven to 375 degrees. Place first 4 ingredients in lightly oiled roasting pan and put into the oven. Cook 1 1/2 hours-turning all after 1 hour. Remove from the oven.
Split open potatoes, cool to touch. Remove garlic from skin. Meanwhile, put ham hocks and water into a large soup pot. Bring to boil (skim off any foam); simmer 1 hour. Add split peas, simmer 45 minutes more, all with the lid slightly askew.
Remove ham hocks from the soup; when cool enough, remove meat from ham hocks, dice and put ham hocks back into the pot. Put roasted vegetables into food processor; add butter and next 5 ingredients. Process well.
Add cream, process and stir all into the soup pot. Stir in diced ham and zest; simmer. Serve, sprinkled with parsley and pass a bowl of potato sticks for garnish if you would like.