Combine corned beef, potatoes, whipping cream, onion, parsley, salt, and pepper in a large mixing bowl; mix well.
Melt butter in a large skillet over low heat. Add corned beef mixture; press flat with a spatula. Cook, uncovered, over medium heat 15 minutes; stir once, and press flat again. Cook, uncovered, 15 minutes.
Make 6 indentions on top of hash mixture using back of a spoon. Add 1 egg to each indention. Cover skillet and cook an additional 5 minutes or until eggs reach desired degree of doneness. Serve immediately.