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1
Preheat oven to 325F with rack in middle.
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2
Pat pork dry and sprinkle with 3/4 teaspoon salt.
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3
Roast in a small flameproof roasting pan tightly covered with foil, covered, 2 hours.
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4
Uncover and continue roasting until some of the meat begins to pull apart easily, 1 to 2 hours more.
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5
Transfer pork to a cutting board and cool slightly.
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6
Pull pork into small pieces and coarsely chop.
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7
Cook orecchiette in a large pot of boiling salted water (2 tablespoons salt for 6 quarts water) 8 minutes (pasta will not be fully cooked).
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8
Reserving 2 cups pasta-cooking liquid, drain pasta in a colander.
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9
Pour off all but 3 tablespoon fat from roasting pan and place pan over medium-high heat.
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10
Add onion, celery, and 1/2 teaspoon each of salt and pepper.
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11
Cook, stirring occasionally, until softened, about 8 to 10 minutes.
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12
Add garlic and oregano and cook, stirring, 3 minutes.
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13
Add tomato paste and cook, stirring, 3 minutes.
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14
Stir in wine, broth, beans, vinegar, and pork.
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15
Transfer to pasta pot and simmer uncovered for 30 minutes, stirring occasionally.
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16
Add 1 cup reserved cooking liquid and bring to a simmer, then add orecchiette and cook, stirring occasionally, until al dente.
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17
Remove from heat and stir in cheese and olive oil.
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18
Season with salt and pepper and thin sauce with additional cooking liquid if necessary.
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19
Serve with additional cheese.
