Place the beef in a bowl or pot large enough to hold it without crowding.
Add the parsley, celery, carrot, onion and garlic.
Pour in enough wine to nearly cover the beef.
Cover and allow to marinate for eight hours at room temperature, or overnight in the refrigerator.
At cooking time, remove the beef from the marinade, shaking and scraping off any vegetables that have clung, and pat it dry with paper towels. Reserve the marinade.
Heat a large pot over medium-high heat.
When the pot is well heated, add enough olive oil to cover the bottom, then add the beef, taking care to avoid spattering.
Brown the beef all over lowering the heat if necessary as the beef begins to render its own fat.
When the beef is well browned, pour in the marinade, raise the heat to high and boil for two or three minutes to evaporate the alcohol from the wine.
Lower the heat to medium-low or even low, depending on your stove, partially cover the pot, then allow the beef and braising liquid to just barely bubble for 2 1/2 to three hours. The beef should be nearly falling apart when done.
At the end of the cooking time, remove the beef to a platter and cover with aluminum foil while you make the sauce.
Raise the heat to medium-high and add the tomato paste dissolved in wine.
Stir to combine well with the braising liquid and cook for two to three minutes.
Pour the contents of the pot into a blender or food processor and puree for about one minute.
Pour the sauce into a gravy boat, or any other serving piece, taste for salt and pepper and add to your taste.
To serve family-style, carve the beef into slices about 3/4 in. thick and cover with several tablespoons of sauce.
Surround the beef with vegetables and potatoes and pass the platter and the sauce at the table.
Otherwise, carve the beef on a cutting board and serve two slices per person along with whatever else you have prepared for dinner.
Garnish with the chopped parsley and pass the sauce separately at the table.