In a large bowl, mash 1 cup of the potatoes with a fork. Add the remaining potatoes, corned beef, cooking liquid, onion , garlic, mustard, parsley, thyme , and nutmeg . Season generously with pepper and mix well. Store in the refrigerator overnight or at least 3 hours. Set up for poaching the eggs: Combine the water, vinegar , and salt in a large skillet and bring to a gentle simmer . Preheat a large well-seasoned cast-iron skillet over medium-high heat. Add 1/4 cup of the butter and heat. When the foaming subsides, add the hash mixture and cook, stirring, for 30 seconds. Using a spatula , press the mixture down into a cake the size of the skillet. Cook, shaking the skillet occasionally, until the hash begins to brown, about 4 minutes. Reduce the heat to medium and continue cooking, shaking the skillet to loosen the hash 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 . Return the skillet to the medium-high heat; add 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. While the corned beef hash is cooking, crack an egg into a cup and carefully slide it into the hot poaching liquid. Quickly repeat with all the eggs. Poach the eggs, turning them occasionally with a spoon, until the whites are firm, or to the desired degree of doneness, about 3 to 5 minutes. Using a slotted spoon, remove the eggs and transfer to a kitchen towel. Lightly dab the eggs with the towel to remove any excess water. Divide the hash among 4 plates and top with the poached eggs. Serve immediately. Copyright 2001 Television Food Network, G.P. All rights reserved
