In a large skillet, cook hash browns in butter until almost tender. Stir in onions, peppers and seasonings. Cook until hash browns are lightly browned and peppers are tender. Add corned beef; heat through.
Meanwhile, place 2-3 in. of water in a large skillet with high sides; add vinegar. Bring to a boil; reduce heat and simmer gently. Break cold eggs, one at a time, into a custard cup or saucer; holding the cup close to the surface of the water, slip egg into water.
Cook 4 eggs, uncovered, until whites are completely set, about 4 minutes. With a slotted spoon, lift each egg out of the water. Repeat with remaining eggs.
Serve over hash mixture. Sprinkle with additional Cajun seasoning and serve with hot pepper sauce if desired. Yield: 4 servings.