Heat olive oil in a large skillet over medium-high heat.
Add the ground beef and cook until browned, breaking it into small crumbles with a spatula; drain excess grease from the pan.
Add the diced onion to the skillet and sauté for 4 minutes until translucent.
Stir in the garlic and dry orzo pasta, cooking for 2 minutes to lightly toast the grains.
Incorporate the tomato paste, dried oregano, salt, and pepper, stirring for 1 minute.
Pour in the diced tomatoes and beef broth, then bring the mixture to a boil.
Reduce the heat to low, cover the skillet, and simmer for 10 to 12 minutes or until the orzo is tender and most liquid is absorbed.
Remove from heat and stir in the baby spinach until wilted.
Fold in the Parmesan cheese and serve immediately.