Cook potatoes in boiling salted water to cover until just tender, about 3 minutes, then drain. Pulse corned beef in a food processor until coarsely chopped.

Sauté onion and bell pepper in butter in a 12-inch nonstick skillet over moderately high heat, stirring, until lightly browned, about 5 minutes.

Add potatoes and sauté over moderately high heat, stirring occasionally, until browned, about 5 minutes. Stir in corned beef and salt and pepper to taste, then cook, stirring occasionally, until browned. Add cream and cook, stirring, 1 minute.

If desired, make 4 holes in hash and break 1 egg into each. Cook over moderately low heat, covered, 5 minutes, or until eggs are cooked to desired doneness, and season with salt and pepper. Sprinkle hash with parsley.