Brown the beef. Add the ground beef to a Dutch oven or soup pot. Break it apart slightly with a spoon, then cook over medium-high heat without stirring for 5–6 minutes so the meat has an opportunity to develop an even brown exterior.
Cook with the onion. Add the finely diced onion to the browned beef. Stir while breaking the meat into smaller pieces, then continue cooking for another 5 minutes. If the beef releases a large amount of fat, carefully spoon off some of the excess; otherwise, it may remain in the pot for additional flavor.
Add the seasonings and orzo. Stir the minced garlic, crushed red pepper, Italian seasoning, and dry orzo into the beef mixture. Cook for approximately 1 minute, stirring so the aromatics become fragrant and the pasta begins to toast lightly.
Incorporate the liquids. Pour in the tomato sauce, beef stock, heavy cream, and Worcestershire sauce. Bring the mixture to a gentle bubble, then cook uncovered for 10 minutes.
Stir during simmering. Mix the orzo frequently while it cooks to prevent the pasta from adhering to the bottom of the pot. Adjust the burner to medium or medium-low as necessary to maintain a steady, gentle simmer rather than a rapid boil. This allows the orzo to become tender without reducing the sauce too quickly.
Add the Parmesan and spinach. Remove the pot from the heat. Stir in the grated Parmesan and fresh spinach until evenly incorporated.
Rest and season. Cover the pot and leave it undisturbed for 3–5 minutes. During this time, the sauce will thicken and the spinach will wilt. Taste and adjust with salt and black pepper as needed.
Serve. Once the sauce has reached the desired consistency, portion the ground beef orzo and serve immediately while hot.