Heat the olive oil in a large skillet over medium-high heat.
Add the ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes.
Add the chopped onion and minced garlic to the skillet. Cook for 3-4 minutes until the onion is softened.
Stir in the orzo pasta and cook for 1-2 minutes, allowing it to toast slightly.
Pour in the beef broth and water, then add the dried oregano, salt, and black pepper. Stir to combine.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 10-12 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Stir in the cherry tomatoes and chopped spinach. Cook for an additional 2-3 minutes until the spinach is wilted and the tomatoes are slightly softened.
Remove the skillet from heat and stir in the grated Parmesan cheese and chopped fresh parsley.
Serve hot, garnished with extra parsley or Parmesan if desired.