Combine the milk with 2 cups water in a medium heavy-duty saucepan and bring to a boil over medium-high heat (watch carefully to prevent a boilover). Add 1-1/2 teaspoons salt and whisk in the cornmeal in a fine stream. Continue to whisk until the polenta begins to thicken, 1 to 3 minutes. Reduce the heat so that the polenta slowly bubbles and cook, uncovered, stirring frequently, until tender and no longer gritty, 20 to 40 minutes, depending on the cornmeal. If the polenta becomes too thick in the process, add milk, a little at a time, to maintain a soft consistency. When the polenta is done, stir in the Parmigiano and 1/2 tablespoons of the butter and season to taste with salt. Keep warm until serving. (The polenta will thicken as it sits. If necessary, add a splash of milk to thin it just before serving.)

Heat the oil in a 10-inch straight-sided saute pan over medium heat. Add the carrots, celery, onion, pepper flakes, and a generous pinch of salt and cook, stirring often, until tender and starting to brown, 8 to 10 minutes. Add the tomatoes and garlic and cook, stirring, for another minute. Add the pork and chicken broth. Bring to a boil and then lower the heat to maintain a simmer. Cook until the broth has reduced by half, about 10 minutes. Stir in the remaining 1 tablespoon butter. Season to taste with salt and pepper.

Spoon the polenta into shallow bowls and then spoon the ragout on the top and to one side, with the broth pooling around the polenta. (Make sure each portion gets a fair share of broth.) Sprinkle each portion with parsley and Parmigiano and serve immediately.

Combine 2 tablespoons salt and 2 teaspoon pepper in a small bowl and rub the mixture all over the pork. Put the pork, fat side up, in a large roasting pan (about 12x16x3 inches). Cover and refrigerate overnight or for up to 3 days.

Remove the pork from the refrigerator and let sit at room temperature for 1 to 1-1/2 hours before cooking.

Position a rack in the center of the oven and heat the oven to 300 degrees F. Uncover the pork and roast until tender everywhere but the very center when pierced with a fork, 4 to 4-1/2 hours. Add the onion, carrots, garlic, wine, and 1 cup water to the roasting pan and continue to roast, stirring the vegetables occasionally, until the pork is completely tender, about 1 hour more.

Remove the roast from the oven and raise the oven temperature to 375 degrees F. Using tongs, separate the pork into 8 to 10 large, rustic chunks and spread out on the pan. If most of the liquid has evaporated, add a splash more water to the pan to create a little more juice. (It shouldn't be soupy.) Return the pork to the oven and continue to roast until nicely browned on the newly exposed surfaces, about 15 minutes. Remove the pan from the oven, transfer the meat and vegetables to a serving platter, and tent loosely with foil. Let rest for 20 minutes. Skim the excess fat from the juices and serve the juices with the vegetables and meat.