In a large stewing pot, heat the extra-virgin olive oil, and sear the beef for a few minutes. Season with salt and pepper. Remove the beef from the pot, and add the chopped carrots, celery, and onion. Cook for 2 minutes, or until the vegetables have become soft. Add 1 cup of red wine, and let it reduce.
Add the potatoes to the pot, and season with salt and pepper. Throw the seared beef back into the pot, and then add the tomato puree, and the remaining wine. Let the liquid come to a boil, and then reduce the heat to medium-low. Simmer until the meat is very tender and the liquid reduced, for an hour and a half more. Add a little water if the liquid cooks down too fast.