Preheat the oven to 425 degrees F (220 degrees C).
For the roasted pig: Mash together the salt, peppercorns, rosemary, garlic and thyme with a mortar and pestle or in a food processor. Slowly add the olive oil to make a paste.
Score the skin of the pig and rub with the herb mixture, making sure to get inside the skin. Place the pieces of meat in a large roasting pan. Add the shallots, garlic heads and 2 cups (500ml) water to the pan. Cover with foil. Roast for about 2 1/2 hours. Remove the foil during the last 30 minutes of cooking and baste often with the pan drippings until the skin is crispy and golden brown.
For the rapini: Saute the rapini in butter and season with salt and pepper. Keep warm.
Serve the roasted pig with a ladle of Mushroom Stew and the rapini.
Place the dried mushrooms in a bowl and cover with water. Let soak for about 15 minutes.
Heat some oil in a cast-iron casserole over medium heat. Add the shallots and saute until softened, about 5 minutes. Add the button mushrooms and cook until browned, about 5 minutes. Add the garlic, and then the ketchup, and continue cooking for a few minutes.
Strain the rehydrated mushrooms and reserve the soaking liquid. Give the mushrooms a quick chop and add to the pan. Cook for 5 minutes. Add the reserved soaking liquid and season with salt and pepper. Cook until the sauce has thickened, about 20 minutes.
To serve, sprinkle with parsley and garnish with pecorino.
Ask your butcher to cut the suckling pig for you.