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1
Remove the thick skin from the pork, leaving a thin layer of fat on top of the meat. Season heavily with salt and place in the refrigerator until ready to use, as long as overnight.
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2
Preheat the oven to 350u00b0F Place a deep saucepan over medium-high heat and add 2 tablespoons olive oil. Gently cook the onion, celery and fennel until they begin to soften, about 10 minutes. Add the stock and thyme and bring to a simmer. Season to taste with salt and pepper.
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3
Rinse pork to remove excess salt, dry with a paper towel and add to seasoned broth. Cover and place in the oven for 90 - 120 minutes, until the meat just begins to pull away from the bone.
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4
Cool meat and broth on the stove top for 30 minutes. Remove the pork and gently pull the meat from the bone, then tear the chunks into bite-size shreds. Place these in a large bowl.
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5
Strain the broth into a separate bowl and then pour enough of it over the meat to barely cover. (Use the rest for soup.) Cover and store in the refrigerator until ready to use.
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6
When ready to make, put a large pot of salted water over high heat and bring to a boil. While the water is heating up, place a large pan over medium-high heat and add the pork and covering liquid. Bring to a boil, then lower heat to medium and cook until the liquid is reduced by half. Add the butter and stir to emulsify into a sauce.
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7
Meanwhile, cook the pasta in salted water according to the directions on the package, 10 to 12 minutes. When it is finished, drain and add to the sauce along with a splash of pasta water. Simmer for 1 minute, then add the lemon juice, half of the cheese, a tablespoon of olive oil and the parsley. Stir to incorporate.
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8
Serve along with remaining cheese.
