Drizzle the beef with 4 to 5 tablespoons of the EVOO and season with a little salt. Place the beef in large Dutch oven with the stock and enough water to just cover. Add the onion, bay leaves and 2 cloves of the garlic. Bring to a low boil and simmer, partially covered, for 2 hours. Stir together the tomato paste and 1/4 cup of the cooking liquid, then add to the pot. Add the pepper and wine and cover. Cook on the stovetop at a gentle simmer until very tender and falling apart, 2 1/2 to 3 hours (alternatively, transfer to the oven and roast at 325 degrees F). Cool and store. Reheat over medium heat or in a moderate oven.
To serve, while the beef is reheating, boil the potatoes until tender and drain. Add the remaining 2 to 3 tablespoons of oil to a pot over medium heat. Add the remaining clove garlic, stir for minute, then remove the garlic. Add the potatoes and crisp a bit. Season with salt, pepper and the rosemary.