Heat olive oil in a large heavy-bottomed skillet or Dutch oven over medium-high heat.
Add the ground beef and cook for 5-7 minutes until fully browned, using a spatula to break the protein into small, uniform crumbles.
Add the minced onion and cook for 3 minutes until translucent, then incorporate the garlic and tomato paste, stirring for 60 seconds until fragrant.
Add the dry orzo pasta to the skillet and toast for 2 minutes, stirring constantly to coat the grains in the rendered fat and aromatics.
Pour in the beef broth, salt, and pepper; increase heat to bring the mixture to a boil.
Reduce the heat to low, cover the vessel with a tight-fitting lid, and simmer for 10-12 minutes until the liquid is fully absorbed and the orzo is tender.
Remove from heat and allow the dish to rest, covered, for 5 minutes to allow residual moisture to distribute evenly before serving.