Preheat the oven to 350 degreesF.
Slice the peppers in half from the stem end down through the base. Remove all the seeds and membranes.
Meanwhile, heat the 2 tablespoons of oil over medium heat in a large nonstick skillet. Add the onion and cook until soft for 3- 4 minutes.
Grate the carrot. Use a grater to shred the carrot.
Add the carrot in the skillet, then ground chicken. Season with salt,and bleak pepper and increase the heat to medium-high.
Reduce the heat to medium-low and cook, uncovered until the meat is cooked through, 2 to 3 minutes. Add the rice and 1/2 cup of water. Let simmer for about 5 minutes. Add the chopped parsley.
Spoon the mixture into each pepper and top with mozzarella cheese, then cover the baking dish with foil, and place in the oven.
Bake for 50 minutes total: 40 minutes covered with foil so the peppers can slightly steam and become tender, and then 10 minutes longer uncovered, so the cheese can get all golden brown and bubbly.
