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1
In a large bowl, mash 1 cup of the potatoes with a fork.
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2
Add the remaining potatoes, corned beef, cooking liquid, onion, garlic, mustard, parsley, thyme, and nutmeg.
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3
Season generously with pepper and mix well.
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4
Store in the refrigerator overnight or at least 3 hours.
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5
Set up for poaching the eggs: Combine the water, vinegar, and salt in a large skillet and bring to a gentle simmer.
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6
Preheat a large well-seasoned cast-iron skillet over medium-high heat.
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7
Add 1/4 cup of the butter and heat.
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8
When the foaming subsides, add the hash mixture and cook, stirring, for 30 seconds.
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9
Using a spatula, press the mixture down into a cake the size of the skillet.
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10
Cook, shaking the skillet occasionally, until the hash begins to brown, about 4 minutes.
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11
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.
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12
To flip the hash, set a plate the size of the skillet on top of the pan.
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13
Invert the pan so the hash falls on to the plate as an intact cake.
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14
Return the skillet to the medium-high heat; add the remaining 1 tablespoon butter.
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15
When the foaming subsides, slide the hash into the skillet cooked-side up.
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16
Cook, shaking the skillet occasionally, for 3 minutes.
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17
Reduce the heat to medium and cook, shaking the skillet occasionally, until the underside is browned and crispy, about 5 minutes more.
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18
While the corned beef hash is cooking, crack an egg into a cup and carefully slide it into the hot poaching liquid.
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19
Quickly repeat with all the eggs.
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20
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.
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21
Using a slotted spoon, remove the eggs and transfer to a kitchen towel.
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22
Lightly dab the eggs with the towel to remove any excess water.
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23
Divide the hash among 4 plates and top with the poached eggs.
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24
Serve immediately.
