1.Preheat the oven to 425°F and set an oven rack in the middle position.
2.In a medium bowl, using your hands, mash the beef with 1 teaspoon salt and baking soda. Let sit for 20 minutes.
3.Line a 9x13-inch baking dish with foil. Place the peppers, cut side up, in the baking dish; drizzle with 1 tablespoon of the oil and sprinkle with ¼ teaspoon salt. Roast the peppers for about 20 minutes, until slightly browned and tender-crisp.
4.Meanwhile, heat the remaining 2 tablespoons of oil over medium heat in a large nonstick skillet. Add the onion and cook, stirring frequently, until soft and translucent, 3 to 4 minutes. Add the garlic and cook 1 minute more.
5.Add the ground beef mixture, chili powder, cumin, and oregano and increase the heat to medium high. Cook, breaking the meat up with a wooden spoon, until the meat is browned and almost cooked through, 4 to 5 minutes.
6.Add the tomato sauce and bring to a boil; reduce the heat to medium low and cook, uncovered, until the meat is cooked through, 2 to 3 minutes. Add the rice and ¾ cup of the cheese, and stir until melted. Remove the skillet from the heat.
7.Remove the peppers from the oven and spoon the meat filling evenly into the peppers. Sprinkle with the remaining ¾ cup cheese and place back in the oven. Roast for 10 to 15 minutes, until the filling is hot and the cheese is melted and bubbling, and serve.