Warm the olive oil in a heavy-bottomed pot or Dutch oven over medium heat. Add the chopped onion and sauté for about 3–4 minutes until it becomes translucent. Stir in the garlic and cook for an additional minute until aromatic.

Incorporate the ground beef into the pot, breaking it apart with a wooden spoon. Cook thoroughly until browned. Drain off any rendered fat to avoid greasiness.

Pour in the tomato purée, diced tomatoes along with their liquid, and beef broth. Mix in the Worcestershire sauce, paprika, Italian herbs, salt, and black pepper. Stir everything well and bring to a low boil.

Add the uncooked elbow pasta to the simmering mixture. Reduce heat to medium-low, cover with a lid, and let simmer gently for 12–15 minutes. Stir occasionally to prevent sticking and ensure the pasta cooks evenly and the sauce thickens.

Remove the pot from the heat source. If using, fold in the shredded cheddar cheese for a rich and creamy consistency. Allow the dish to rest uncovered for 5 minutes to further thicken.

Spoon the goulash into serving bowls and sprinkle with chopped parsley, if using, before serving warm.