Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil. Add the bell peppers and cook for 3 minutes to soften slightly. Remove and drain upside down on paper towels.
In a large skillet over medium heat, cook the ground beef until browned, breaking it up with a spoon, about 5-7 minutes. Drain any excess fat.
Add the chopped onion, carrot, and garlic to the skillet. Cook for 4-5 minutes until the vegetables are softened.
Stir in the cooked rice, peas, tomato sauce, oregano, basil, salt, and black pepper. Cook for 2 more minutes, stirring to combine well.
Remove the skillet from heat and spoon the beef and rice mixture evenly into each bell pepper.
Place the stuffed peppers upright in a baking dish. Cover the dish with foil.
Bake in the preheated oven for 30 minutes.
Remove the foil and sprinkle the shredded cheddar cheese evenly over the top of each stuffed pepper.
Return to the oven and bake uncovered for an additional 5 minutes, or until the cheese is melted and bubbly.
Let the stuffed peppers cool for 5 minutes before serving.