Preheat oven to 325°F.
Season the meat all over with salt and pepper. Place the flour on a large plate or platter. Dredge the meat in the flour, shaking off the excess.
Use a mallet, or any blunt object, to pound the flour into the meat and to thin the meat to about ¼ inch in thickness. Dredge in the flour once again, shaking off any excess.
Heat the bacon grease (or oil) in a large pot (with lid) over medium-high heat. Working in a couple of batches, add the prepared steaks to the pot. Cook until browned on the underside, about 2 to 3 minutes. Flip and cook until both sides are nicely browned and slightly crisp, about 4 to 5 minutes total. Repeat with remaining steaks. Set aside.
Add the onions, carrots, and celery to the pot and cook until soft, about 5 minutes. Add the garlic and cook for another 30 seconds, stirring occasionally.
Stir in the tomato paste and cook for about 2 minutes.
Use your hands to squeeze the tomatoes into the mixture. Add the beef broth, thyme, oregano, Worcestershire sauce, bay leaves, 1½ tsp salt, and 1 tsp black pepper.
Nestle the steaks into the liquid and press so they are submerged.
Cover the pot and place it in the oven. If you went with cutlets/steaks, roast for 1½ hours. If you opted for one whole piece of meat, then cook for about 2¼ hours, or until the meat is very tender when pierced with a fork.
Remove from oven and carefully transfer the steaks (or roast) to a platter and then pour about half of the sauce over the top. Serve the remaining sauce tableside. Garnish with chopped parsley.