Melt butter in large deep skillet on medium heat. Add potatoes; cook 10 min. or until lightly browned, stirring occasionally. Meanwhile, mix milk and mustard until blended.
Add milk mixture to potatoes along with the corned beef; cook 2 min., stirring occasionally. Use back of large spoon to make 4 indentations in potato mixture. Slip cracked egg into each indentation; cover skillet. Cook 4 min. or until egg whites are firm and yolks are cooked to desired doneness.