Preheat the grill to medium heat (about 375°F to 400°F).
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the chopped onion and cook until softened, about 3-4 minutes.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Add the ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 6-8 minutes. Drain any excess fat.
Stir in the cooked rice, diced tomatoes, Italian seasoning, salt, black pepper, and half of the chopped parsley. Cook for 2-3 minutes until heated through and well combined. Remove from heat.
Stir in the shredded mozzarella cheese and half of the Parmesan cheese into the beef mixture.
Brush the outside of the bell peppers and the cut edges with the remaining 1 tablespoon of olive oil.
Fill each bell pepper cavity with the beef and rice mixture, pressing down gently to pack the filling.
Sprinkle the remaining Parmesan cheese on top of each stuffed pepper.
Place the stuffed peppers upright on the grill. Close the grill lid and cook for 20-25 minutes, turning occasionally to prevent burning, until the peppers are tender and slightly charred.
Remove the stuffed peppers from the grill and let them rest for 5 minutes.
Garnish with the remaining fresh parsley before serving.