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1
Remove the pork from the refrigerator and let it sit at room temperature for 30 minutes.
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2
Pat dry with paper towels and season with the measured salt and pepper; set aside.
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3
Place the milk, garlic, shallot, thyme, and bay leaf in a large heavy-bottomed pot or Dutch oven and bring to a simmer over medium-high heat.
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4
Reduce the heat to low, add the pork, cover with a tightfitting lid, and cook for 75 minutes.
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5
Turn the pork over and continue cooking for another 75 minutes.
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6
Uncover and cook until the pork is fork-tender and easily shreds, about 30 minutes more.
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7
Transfer the pork to a cutting board.
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8
Increase the heat to medium high and cook the braising liquid, stirring occasionally and scraping the bottom of the pot to release any browned bits that have accumulated, until the liquid has reduced by half, about 25 minutes.
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9
(The sauce will look lumpy and curdled.)
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10
Meanwhile, prepare the meat and pasta.
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11
Using 2 forks, shred the pork into bite-sized pieces, discarding any large pieces of fat or bone; set the meat aside.
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12
Bring a large pot of heavily salted water to a boil over high heat.
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13
Add the pasta and cook until just heated through and al dente.
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14
Drain, reserving 1 cup of the cooking water, and set aside.
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15
Remove and discard the thyme sprigs and bay leaf from the reduced braising liquid and transfer the liquid to a blender.
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16
Remove the small cap from the blender lid (the pour lid) and blend on high speed until smooth, covering the space with a kitchen towel (this allows steam to escape and prevents the lid from popping off).
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17
Alternatively, use an immersion blender.
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18
Return the sauce to the pot, add the shredded pork and cooked pasta, and stir to evenly combine, adding the reserved pasta cooking water as needed.
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19
Taste and season with salt and pepper as needed.
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20
Serve immediately.
