Preheat oven to 375 degrees F.
Cut off the tops of the peppers and remove the seeds and the membranes; set the tops aside. Rub the peppers inside and out with the oil, then sprinkle the insides with the salt. Place the peppers cut side down, on a rimmed baking sheet pan. Bake until tender, 15-20 minutes.
Meanwhile, make the filling. Cut around the stems of the reserved pepper tops to remove them. Dice the tops and set aside.
Heat the oil in a large skillet over medium heat. Add the ground chicken and cook, stirring often to crumble it, until nicely browned, about 8 minutes. Remove from the pan and set aside.
Add the butter to the skillet, still over medium heat. Add the diced pepper tops, onions, and garlic and saute until the vegetables are soft and translucent, about 5 minutes.
Stir in the rice, green chiles, marinara sauce, cumin, oregano, salt and pepper. Cook until the rice is tender. Stir in the cooked chicken and ½ cup of the cheese, if using.
Nestle the cooked peppers, cut side up, in a medium baking dish. Evenly spoon the filling into the peppers. If desired, spread a spoonful of sauce over the filling in each pepper. Cover and bake until heated through, about 20 minutes. If using cheese, uncover, top with remaining ½ cup of cheese, and bake until the cheese is melted, about 5 minutes. Garnish with parsley, if desired and serve immediately.
Store leftover in an airtight container in the refrigerator for up to two days or wrap in parchment, then aluminum foil, seal in a plastic bag and freeze for up to 3 months. Defrost frozen peppers in the refrigerator overnight then reheat on a rimmed baking sheet in a preheated 350 degree oven for 20-30 minutes.