Toss in the smashed garlic cloves in their peels. Use tongs to turn the beef cubes and sear each of the other sides before transferring to a rimmed plate. Add more oil if needed and repeat the searing process with the next third and then the final third of the beef. Return all of the beef to the pan, still over high heat.
As soon as it boils, add the lid, drop the heat as low as it can go, and let it simmer for 2 hours, or until the beef is tender. Remove the lid, stir in the remaining 2/3 cup of Chianti and the freshly ground black pepper, raise the heat to medium, and simmer for about 20 to 30 minutes, or until the sauce is quite thick and a deep mahogany colour. Remove the thyme bouquet (if you used it), the garlic peels, and the bay leaves. This can be served immediately but improves immensely when allowed to rest tightly covered in the refrigerator for 24 hours before serving.