400° oven preheat. Rice should be cooked in a small pot according the directions on the package. Heat oil in a big skillet over medium heat. 5 minutes should be enough time to soften an onion. For approximately a further minute, add the tomato paste and garlic and stir until fragrant. Add the ground beef and cook for 6 minutes, breaking up the meat with a wooden spoon, or until it is no longer pink. Remove fat.
Stir in the cooked rice and diced tomatoes before adding the beef mixture back to the skillet. Add oregano, salt, and pepper for seasoning. Allow to simmer for 5 minutes, or until liquid has somewhat reduced.
In a 9" x 13" baking dish, arrange the peppers cut side up and drizzle with oil. Fill each pepper with the beef mixture, sprinkle Monterey jack cheese on top, and then cover the baking dish with foil.
About 35 minutes into baking, the peppers should be soft. 10 more minutes of baking are required after removing the cover.