Heat oven to 350°F and position a rack in the center.
Pat beef dry. Season all sides with the salt and black pepper.
Warm olive oil in a Dutch oven over medium-high heat.
Brown the beef in batches until well seared. Transfer to a plate.
Reduce heat to medium. Cook onion until translucent, about 4 minutes.
Stir in garlic for 30 seconds. Add tomato paste and cook until darkened.
Pour in red wine and scrape up browned bits. Reduce by half.
Add crushed tomatoes, broth, oregano, cinnamon, allspice, and paprika. Bring to a simmer.
Return beef and any juices. Cover and simmer gently for 20 minutes.
Stir in the orzo, making sure it’s submerged in the sauce.
Cover and bake 30 to 35 minutes, stirring once halfway through.
Rest 10 minutes. Fold in half the cheese and the parsley. Taste and adjust seasoning.
Serve warm with extra grated cheese on top.