Heat the olive oil in a large skillet over medium-high heat. Add the ground beef and cook for 5 to 6 minutes, breaking it apart with a spoon, until browned. Drain excess grease if needed.
Add the diced onion and cook for 3 to 4 minutes, until it begins to soften. Stir in the garlic and cook for about 30 seconds, just until fragrant.
Stir in the tomato paste, Italian seasoning, paprika, salt, and black pepper. Cook for about 1 minute, stirring often, until the tomato paste coats the beef and the spices become more flavorful.
Add the crushed tomatoes and stir well. Add the dry orzo directly to the skillet, then pour in the beef broth. Stir everything together and bring to a gentle simmer.
Reduce the heat to medium-low and cook for about 13 minutes, stirring often, until the orzo is tender and has absorbed most of the liquid.
Pour in the heavy cream and stir until the sauce turns smooth and creamy. Add the Parmesan cheese and stir gently until melted into the sauce.
Remove from the heat and let the orzo rest for 3 to 5 minutes so the sauce thickens slightly. Finish with fresh parsley and extra Parmesan if desired. Serve warm.