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1
Heat oven to 300 degrees F with rack in the middle.
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2
Blot the pork dry with paper towels (you want to start with dry meat so it will properly brown), and season generously with kosher salt and pepper.
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3
Heat the olive oil in a 5 1/2 quart (or larger) dutch oven or casserole over medium-high heat, and then add the pork in a single layer, being careful not to overcrowd the meat. (You may need to brown the meat in a few batches.) Brown the meat on all sides, about 10 to 12 minutes total. Transfer the browned meat to a plate; set aside. Pour off all but 1 tablespoon of fat from the dutch oven.
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4
Add the onion and fennel seed and saute over medium heat until the onion is translucent, about 5 minutes. As the onion starts to sweat, scrape up any brown bits from the bottom of the pan with a spatula or wooden spoon.
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5
Add the white wine, and stir to deglaze any remaining brown bits. Let reduce at a vigorous simmer for about 1 minute. Add the pork and any juices that have accumulated back to the pan, then add just enough chicken stock to come about 3/4 way up the sides of the pork. Add the strips of lemon zest.
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6
Wet a sheet of parchment paper, crumple it, and cover the pot, pressing down so that the paper nearly touches the meat and the edges hang over the side. Cover the pot, and transfer it to the oven to braise until the pork is very tender, 2 to 2 1/2 hours. Check after 30 minutes to make sure the liquid isn't simmering too vigorously. If it is, lower the oven temperature by 10 or 15 degrees and/or set the lid slightly ajar.
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7
When the pork is done, transfer it to a work surface. Pour the sauce through a fine strainer into a large bowl, discarding all of the solids. Skim off any visible fat with a spoon, or use a fat separator to remove the fat from the sauce.
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8
Remove and discard gristle and any large pieces of un-rendered fat from the pork.
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9
Cook the new potatoes in a large pot of boiling, well-salted water until they''re just tender (not mushy).
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10
Meanwhile, in a bowl, combine eggs and cheese; whisk together. Season with salt and pepper.
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11
Shortly before serving, heat your oven to 375 degrees F.
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12
Return the pork and sauce to the dutch oven, and warm over low heat. Season the sauce to taste with salt and pepper. Add some lemon juice if more acidity is needed. It's time well spent to taste and tinker until you get the right flavor and balance in your sauce.
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13
Once at a bare simmer, nestle the cooked potatoes among the chunks of pork, then do the same with the frozen peas. Add the egg mixture over the top in an even layer. Tightly cover the pot and return to the oven, about 6 to 8 minutes, or until the eggs just begin to set. Then uncover the pot and cook until the edges of the egg begin to brown, about 10 minutes more (though time may vary). Spoon off any fat that may rise to the top. (The eggs may sink a bit at first, and you might think you've ruined your dish, but carry on -- the eggs will set up and form a slightly golden crust over the pork. Just monitor closely and have faith!) Remove from oven. Scatter fresh tarragon over the top and add lemon juice to taste before serving (or serve with lemon wedges on the side).
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14
If preparing this dish in advance, complete steps 1 -through 8, placing the meat in a tall container and pouring the braising liquid on top. Refrigerate. The following day, lift off the congealed fat and discard. Let the meat come to room temperature. About 1/2 hour before serving, place the meat in an ovenproof dish in a 325 degree F oven with the braising liquid. The pork will take about 30 minutes to reheat. Then, proceed with steps 9 through 13.
