Place a 10-inch nonstick sauté or cast iron pan over medium-high heat. Heat the olive oil and add diced potatoes.
Sauté for 15 minutes until potatoes begin to brown slightly and begin to become tender.
Add the shallots and brussels sprouts sauté for 5 minutes.
Add corned beef, sauté for 3 minutes longer.
Stir in cream, worcestershire sauce, salt and pepper. Simmer until most of the liquid has evaporated and the cream has thickened enough to bring the hash together (about 5 minutes).
In a separate sauté pan, fry the eggs in melted butter over medium heat.
Toast bread and cook eggs to desired doneness.
Spoon hash onto plates and serve topped with egg and toast on the side.