Wash and scrape the potatoes; leave them whole. Pour oneinch of stock into a saucepan and bring to a boil. Add the potatoes and salt, cover, and bring again to a boil. Cook for fifteen to twenty minutes, depending on the size of the potatoes.
Add the butter and pepper. Mix the cornstarch with the water and add to the liquid around the potatoes. (There will be only a little.) Cook for one minute, or until slightly thick and transparent. Turn potatoes out onto a serving dish and garnish with chopped parsley.