Heat the oven to 375°F. Combine rice and its water in a saucepan, bring to a boil, cover and cook over low heat for 15 to 18 minutes; rest covered for 5 minutes.
While the rice cooks, brush pepper halves with 1 teaspoon oil and arrange cut-side up in a 9-by-13-inch baking dish. Bake empty for 12 minutes.
Meanwhile, heat remaining oil in a skillet and brown beef and onion for 7 to 8 minutes until the beef reaches 160°F. Drain excess fat, then stir in garlic for 30 seconds.
Add 3/4 cup tomato sauce, salt, oregano and pepper and simmer for 3 minutes. Fold in the cooked rice and divide the filling among the softened pepper halves.
Pour remaining tomato sauce around the peppers, top each with cheddar and bake for 20 to 25 minutes until tender with the filling at 165°F. Rest for 5 minutes and serve two halves per person.