Set the oven rack to the lower third of the oven. Preheat to 325°F (163°C).
Season each steak on both sides with salt and pepper.
Place flour (1/2 cup) in a shallow dish. Dredge each piece of steak in flour on both sides, pressing to coat then shaking off excess.
Place dredged meat on a flat surface and tenderize using a needling device, until each slice is 1/4-inch thick.
Heat vegetable (4 tablespoons) oil in a Dutch oven or large ovenproof pot with a tight-fitting lid (also ovenproof). Over medium-high heat, without crowding the pan, (I browned 1 steak at a time) brown beef on both sides, about 2 minutes per side. Remove to a plate and repeat with remaining steaks, adding more oil as needed.
Add onion (1 medium chopped), garlic (4 cloves minced), and celery (3 stalks chopped) to pot and saute, on medium-low, until just tender, about 3-4minutes. Stir in tomato paste (1 tablespoon). Stir in beef broth (1 3/4 cups) and canned tomatoes with juice (14 ounces), scraping the bottom of the pot, to lift up all the brown bits.
Add smoked paprika (1 teaspoon), thyme (1/2 teaspoon), oregano (1 teaspoon), salt (1 1/2 teaspoons), pepper (1 teaspoon), and Worcestershire sauce (1 tablespoon) and mix.
Layer the meat back into the pot so it's submerged by the liquid and cover with the lid. Place in preheated oven and cook until the meat is very tender, 1 1/2-2 hours.