Coarsely chop together the rosemary, sage and thyme, and transfer them to a small bowl. Add 2 tablespoons of the oil, and stir to combine.
Score the fat cap of the pork shoulder in a crosshatch pattern, then rub it all over with 2 1/2 tablespoons salt and 2 teaspoons pepper.
Heat a large skillet over medium-high heat. Add the remaining 3 tablespoons oil, and heat until shimmering. Add the pork, fat-side down, and brown it well, 3 to 4 minutes, then brown it all over, 3 to 4 minutes per side. Transfer the pork to a large plate.
Add the wine, garlic and allspice to the pan, bring to a simmer and reduce by about half. Set aside.
Put the carrots, celery, onions and bay leaves in the insert of a 7-quart slow cooker. Rub the herbed oil all over the pork, being sure to push some into all the natural divisions between muscles; place it on top of the vegetables, and pour in any collected juices. Add the reduced wine mixture and the chicken broth, cover and cook on low for 8 hours.
Transfer the pork to a cutting board, and tent with foil. Transfer the vegetables to a serving platter with a slotted spoon. Discard the bay leaves, and tent the vegetables with foil. Pour the juices into a liquid measuring cup, and let them settle for about 10 minutes. The fat should rise to the surface; spoon off as much as you can, and discard. Pour the juices into a small saucepan, and bring to a boil.
While the juices boil, make a cornstarch slurry: For every cup of juices, mix 1 teaspoon cornstarch into 1 tablespoon cold water until dissolved. Reduce the heat so the juices are simmering, whisk in the slurry and cook, whisking frequently, until the sauce has slightly thickened, about 5 minutes. Stir in 2 tablespoons of the parsley. Season with salt if necessary.
Slice the pork against the grain into 1/4-inch-thick slices, and arrange on a large platter with the vegetables. Ladle some of the sauce on top. Season the meat with a pinch of salt, and garnish with the remaining 2 tablespoons parsley. Serve with egg noodles, and pass the remaining sauce.
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