Instructions: Melt the butter in a large, heavy saucepan or Dutch oven over medium heat.

Add 2 cups of the onions, 3/4 teaspoon of the salt, and 3/4 teaspoon of the pepper. Cook, stirring, until the onions are soft, about 4 minutes. Add the cabbage and the sugar, and stir until slightly wilted, about 3 minutes. Add the mustard and garlic and stir to mix. Add the water, stir, then cover. Cook for 20 minutes, stirring occasionally.

Add the cream, stir to mix, and cook, covered, for 10 minutes. Remove from the heat and keep warm.

In a large nonstick skillet over medium-high heat, heat the oil. Add the remaining 1 1/2 cups onions, the remaining teaspoon of salt, and remaining teaspoon of pepper. Cook, stirring, for 2 minutes. Add the potatoes and spread evenly over the onions. Cook, flipping about every minute, gently mashing until golden brown, about 8 minutes.

Add the corned beef and cook, stirring and pressing the hash browns into it, for 2 minutes. Drop the whole cracked eggs over the mixture, about 1/4 inch apart, reduce heat to low, cover and cook until the eggs are poached, 7 to 8 minutes.

To serve, spread about 1/2 cup of the cabbage in the center of a serving plate and top with a wedge of corned beef hash with an egg. Sprinkle with the parsley.

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