Peel potatoes and cut into 1/2-inch dice. Add potatoes to a large saucepan of boiling water and boil 6 minutes, or until just tender. Drain.
In a large non-stick skillet cook onion and garlic in butter over moderate heat, stirring, until onion is golden.
Add bell pepper and cook, stirring, 5 minutes. Sprinkle flour over mixture and cook, stirring, 2 minutes. Stir in broth, horseradish, and Worcestershire sauce and simmer, stirring, 2 minutes. Add corned beef, potatoes, and salt and pepper to taste and cook over moderate heat, turning hash, until browned and crisp, about 15 minutes.
Serve hash with fried eggs.
To make corned beef:.
In a kettle combine beef with cold water to cover by 2 inches and bring water to just a boil, skimming froth. Simmer beef, covered, 3 hours, or until tender. Remove kettle from heat and let beef stand in cooking liquid 20 minutes. Transfer beef to work surface and trim fat. Use beef as part of a boiled dinner and/or for making corned beef on rye. Corned beef keeps, covered and chilled, 4 days.