Preheat the oven to 300 degrees F.
Place the corned beef in a colander in the sink and rinse well under cold running water.
Place the corned beef in a large Dutch oven with a tight-fitting lid; add the water, bay leaves, peppercorns, allspice, and cloves. Bring to a boil, uncovered, and skim off any scum that rises to the surface. Cover and transfer pan to the oven, and braise until very tender, about 3 hours and 45 minutes.
Transfer the corned beef to a cutting board and cover tightly with foil to keep warm. Add the cabbage and potatoes to the cooking liquid and bring to a boil. Lower the heat and simmer until the vegetables are tender, about 20 minutes.
Using a slotted spoon, transfer the cabbage to a large platter. Slice the corned beef across the grain of the meat into thin slices. Lay the slices over the cabbage and surround it with the potatoes. Ladle some of the hot cooking liquid over the corned beef and season with pepper. Serve immediately with the mustard or horseradish sauce.
For the hash: In large bowl, place 1 cup of the potatoes and mash with a fork. Add the remaining 1 cup potatoes, corned beef, cooking liquid, onion, garlic, mustard, thyme, and nutmeg. Season generously with pepper and mix well. Store in the refrigerator overnight.
Remove the hash mixture from the refrigerator and stir in the parsley.
Heat 1/4 cup butter in a large cast-iron skillet over medium-high heat. When the foaming subsides, add the hash mixture and cook, stirring, for 30 seconds. Using a spatula, press the mixture down into a round cake the size of the skillet. Cook, shaking the skillet occasionally, for 4 minutes. Reduce the heat to medium and continue cooking, moving the skillet occasionally, until the underside is browned and crusty, about 6 minutes more.
To flip the hash, set a plate the size of the skillet on top of the pan. Invert the pan so the hash falls on to the plate as an intact cake. Invert the hash onto another plate, cooked-side up. Return the skillet to the heat, raise to medium-high, and heat the remaining 1 tablespoon butter. When the foaming subsides, slide the hash into the skillet cooked-side up. Cook, shaking the skillet occasionally, for 3 minutes. Reduce the heat to medium and cook, shaking the skillet occasionally, until the underside is browned and crispy, about 5 minutes more. Set aside covered with foil to keep warm.
For the eggs: While the corned beef hash is cooking, combine the water, vinegar and salt in a large skillet and bring to a simmer. Crack the eggs into separate cups. Carefully slide the eggs into the skillet and cook, turning occasionally with a spoon, until firm, about 3 to 5 minutes. Using a slotted spoon, remove the eggs and transfer to kitchen towel. Lightly dab the eggs with a kitchen towel to remove any excess water.
Divide the hash among plates and top with the poached eggs.
In a small bowl, mix together the mayonnaise, sour cream, horseradish, zest, and 2 teaspoons salt. Season generously with pepper to taste. Refrigerate the horseradish sauce for at least 30 minutes before serving.
Leftover corned beef makes great corned beef hash. In fact, most of us here in the Food Network Kitchens make it just to make our morning-time favorite, corned beef hash with poached eggs.
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