Using the back of a knife and working over a medium bowl, scrape the corn cobs to release any pulp and juices; reserve the cobs.
In a medium soup pot, heat the oil. Add the onion and cook over moderate heat until softened, about 6 minutes. Add 3 cups of water, the ham rind and the corn cobs, pulp and juices and bring to a simmer. Cook over moderately low heat for 5 minutes; discard the cobs and ham rind. Add the cream and potatoes, bring to a simmer and cook until the potatoes are almost tender, about 5 minutes. Add the corn kernels and ham and simmer until the corn and potatoes are tender, about 5 minutes longer. Season with salt and pepper, ladle into bowls and serve.