1.Melt butter in a large deep skillet over medium heat.
2.Add potatoes; cook 10 minutes or until lightly browned, stirring occasionally. Meanwhile, finely chop corned beef. Combine half and half and mustard; mix well. Stir corned beef and mustard mixture into potatoes; cook 2 minutes. With the back of a large spoon, make four indentations in potato mixture. Drop eggs into indentations; sprinkle with salt and freshly ground black pepper, if desired. Cover skillet; cook about 4 minutes or until eggs are cooked to desired doneness. Serve with ketchup or chili sauce, if desired.