Place each beef slice between 2 sheets of plastic wrap and. using a meat pounder, pound until ½  inch thick. Place 1 ham slice on top of each beef slice, and then top with a cheese slice.

In a small bowl, mix together the parsley, 2 teaspoons of the garlic, 1 tablespoon of the carrot and the 4 teaspoons celery. Sprinkle the mix­ture evenly over the center of each cheese slice. Beginning at one end of each beef slice, tightly roll up and secure the seam with toothpicks. Seal the ends with toothpicks as well, to keep the filling from spilling out.

In a deep saucepan over medium heat, warm the olive oil. Add the beef rolls and brown well on all sides, 4-5 minutes. Reduce the heat to medium-low, add the remaining 2 tablespoons carrot, 2 tablespoons celery and the onion and sauce for 2 minutes. Add the remaining 2 teaspoons garlic and sauce until fragrant, 1-2 minutes.

Raise the heat to high, add the ½ cup red wine, and deglaze the pan by stirring to dislodge the browned bits from the pan bottom. Boil for 1 minutes, then add the tomato purée. Return to a boil, then reduce the heat to low and simmer, uncovered, until the beef is tender when pierced with a fork, about 1½ hours.

Add the remaining 2 tablespoons red wine and continue to simmer for 2 minutes longer. Season to taste with salt and pepper. Spoon onto warmed individual plates, remove the toothpicks, and serve immediately.