Combine the chiles, garlic, kosher salt, and paprika in a food processor and pulse until a paste is formed. Transfer the chile mixture to a large nonreactive bowl and add the wine, tomato paste and olive oil. Stir well to blend.
Using a sharp paring knife, make deep slits all over the roast to allow the marinade to penetrate the meat. Add the pork to the bowl and turn to coat with the marinade. Cover with plastic wrap and refrigerate overnight, turning occasionally.
Preheat the oven to 350 degrees F and bring the meat to room temperature.
Remove the meat from the marinade and transfer to a roasting pan, preferably a pan just large enough to hold the meat. Add the chicken stock to the roasting pan (it should come 1 inch up the sides of the pan) and transfer to the oven. Bake the meat for 1 1/2 hours, turning occasionally, or until browned on all sides. Make sure to add water to the roasting pan periodically as necessary during the entire roasting time to keep the drippings from burning on the pan bottom. Reduce the oven temperature to 300 degrees F and continue to cook, turning the meat occasionally, for about 4 1/2 hours longer, or until the meat is fork-tender. Set the meat aside to rest for about 15 minutes. Using a spoon, skim as much fat from the surface of the drippings as possible. Using 2 forks, pull the meat into serving-size pieces and toss with the pan juices. Season with salt to taste, if necessary, and serve either hot or warm, with the Portuguese White Beans and Portuguese Rice.
