2 cups diced cooked beets (2 or 3 beets, weighing about 1 pound)
1 egg, lightly beaten
1 teaspoon Worcestershire sauce
Freshly ground black pepper, to taste
1/4 teaspoon ground nutmeg
1/2 tablespoon olive oil
1-1/2 pounds russet potatoes, peeled and diced
2 tablespoons vegetable oil
2 tablespoons white wine vinegar
Freshly ground black pepper, for garnish
Melt the butter in a sauté pan or skillet and sauté the onion and bell peppers over medium-high heat for 5 minutes. Transfer to a mixing bowl and add the corned beef, beets, eggs, Worcestershire sauce, pepper, and nutmeg. Mix thoroughly and let rest in the refrigerator for at least 5 hours or overnight.
Heat the olive oil in a sauté pan, add the potatoes, and sauté over medium-high heat for 8 to 10 minutes, or until golden brown, stirring frequently. Set aside.
Heat 1/2 tablespoon of the vegetable oil in each of 2 large sauté pans. Add one quarter of the hash mixture to each pan and cook over medium heat for about 2 minutes. Add the sautéed potatoes and continue cooking for 6 to 8 minutes or until crispy, shaking and flipping the pan or stirring frequently with a spatula. Remove and keep warm while repeating for the remaining hash mixture.
Bring a medium saucepan of salted water to a boil and add the vinegar.
Break 4 eggs, one at a time, into a saucer and then slip carefully into the pan.
Cook until the egg whites are set and firm, about 4 minutes.
Remove with a slotted spoon and let drain.
Repeat for the remaining 4 eggs.
To serve, place the hash on warm serving plates, top with a poached egg, and garnish with freshly ground black pepper.