Preheat the grill to medium heat (about 350°F to 400°F).
In a large skillet, heat 1 tablespoon of olive oil over medium heat.
Add the chopped onion and minced garlic to the skillet and sauté for 3-4 minutes until softened.
Add the ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes.
Stir in the diced tomato, cooked rice, dried oregano, salt, and black pepper. Cook for another 2 minutes to combine flavors.
Remove the skillet from heat and stir in the chopped parsley and half of the shredded cheddar cheese.
Drizzle the inside of each bell pepper with the remaining 1 tablespoon of olive oil.
Fill each bell pepper with the beef and rice mixture, pressing gently to pack the filling.
Spoon about 2 tablespoons of tomato sauce over the top of each stuffed pepper.
Place the stuffed peppers upright on the grill grates. Close the grill lid and cook for 25-30 minutes, turning the peppers occasionally to prevent burning, until the peppers are tender and slightly charred.
During the last 5 minutes of grilling, sprinkle the remaining shredded cheddar cheese on top of each stuffed pepper and close the lid to melt the cheese.
Remove the stuffed peppers from the grill and let them rest for 5 minutes before serving.