Heat olive oil in a large deep skillet or pot over medium-high heat.
Add ground beef and cook, breaking it apart with a spoon, until browned and cooked through, about 5-7 minutes.
Add chopped onion and minced garlic to the beef. Cook for 2-3 minutes until the onion is softened and fragrant.
Stir in orzo pasta, beef broth, dried oregano, dried basil, salt, and black pepper.
Bring the mixture to a boil, then reduce heat to medium-low and cover.
Simmer for 12-15 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Remove the pot from heat and stir in heavy cream and grated Parmesan cheese until creamy and well combined.
Sprinkle chopped fresh parsley over the dish and serve immediately.