01 - Set oven temperature to 400°F.
02 - Peel the onions, trim the tops, and slice a thin layer off the bottoms so they stand upright.
03 - Carefully scoop out the centers using a spoon or melon baller, leaving a ½ inch shell; finely chop the removed onion flesh.
04 - Heat olive oil in a skillet over medium heat, then add chopped onion flesh, carrot, celery, and garlic. Cook for 4-5 minutes until softened.
05 - Add ground beef and cook until browned, about 5-6 minutes; drain excess fat if necessary.
06 - Stir in tomato paste, thyme, oregano, smoked paprika, salt, and black pepper. Cook for another 2 minutes, then remove from heat.
07 - Fill the hollowed onions with the beef mixture, pressing firmly, and arrange them in a baking dish.
08 - Pour beef broth around the onions and cover loosely with aluminum foil.
09 - Bake for 35 minutes.
10 - Remove foil, sprinkle Parmesan if using, and roast uncovered for 15-20 minutes until onions are tender and tops are golden.
11 - Let rest for 5 minutes, sprinkle with fresh parsley, and serve warm.