Sprinkle the pepper over the short ribs. Heat the olive oil in a Dutch oven or casserole over medium heat. Sear the ribs, 3 or 4 at a time, browning well on all sides. As they are browned, drain them on paper towels.
Preheat the oven to 350°F.
Return half of the ribs to the casserole. Sprinkle with half of the garlic. Layer half of each vegetable over the meat. Add 4 cloves and sprinkle with half of the parsley. Repeat with the remaining ingredients, ending with a layer of chopped parsley.
In a bowl mix together the vinegar, tomato paste, brown sugar, salt, the 1 teaspoon black pepper, and the cayenne. Pour it over the meat and vegetables and then add the beef stock just to cover.
Cover the casserole, set over medium heat, and bring to a boil. Bake on the center rack of the oven for 1½ hours. Uncover and continue baking until the meat is very tender, 1½ hours longer. Taste, correct the seasoning, and serve immediately.