Combine the beef, breadcrumbs, basil, garlic, Pecorino Romano, salt, pepper, eggs and onion in a large mixing bowl. Using your hands, mix all the ingredients until well incorporated. Use immediately or refrigerate for up to 24 hours.
Shape the meatballs with your hands into rounds approximately 2 1/2 ounces each. Coat each meatball with olive oil, then place on a sheet pan. Bake until golden brown and cooked through, 20 to 25 minutes.