Brown the beef: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the ground beef and cook, breaking it into small crumbles, until browned (about 5-6 minutes). Remove with a slotted spoon and set aside. Drain most of the fat, leaving about 1 tablespoon in the pan.
Sauté the aromatics: Add the diced onion to the pan and cook for 3-4 minutes until softened. Add the minced garlic and cook for 30 seconds until fragrant.
Add liquids and orzo: Pour in the crushed tomatoes and chicken broth. Stir in the Italian seasoning, salt, and pepper. Add the orzo pasta and stir to combine.
Simmer: Bring to a boil, then reduce heat to medium-low. Cover and simmer for 10-12 minutes, stirring occasionally, until the orzo is tender and most of the liquid has been absorbed.
Finish the sauce: Stir in the heavy cream and grated parmesan cheese. Add the cooked ground beef back to the pan. Stir everything together and cook for another 1-2 minutes until heated through and creamy.
Serve: Remove from heat and let sit for 2-3 minutes (the sauce will thicken as it rests). Garnish with fresh parsley and extra parmesan. Serve immediately.