MAKE THE SAUCE
Pulse the onions and garlic in your food processor a couple of times. Add the tomatoes (with juice), stock, vinegar, sugar, and oregano, and pulse until puréed.
Heat corn oil in a deep heavy large skillet over medium heat until it shimmers. Add sauce and simmer for 10 minutes. Stir in salt. Keep warm on the stove, or store in an air-tight container if not using immediately.
ROAST THE PEPPERS
Position a rack about 4 inches from the broiler and turn on HIGH.
Set the peppers on a baking sheet and then place under the broiler for 5 minutes. Remove from oven and use tongs to flip the peppers over. Return to the oven and broil for another 5 minutes until smokey and charred all over. Keep an eye on them, as broilers can vary from oven to oven.
Use a small sharp knife to cut a slit on the top of the peppers from the tip to the end of the pepper, careful not to cut too deeply. Let cool slightly, peel off the skins, and use a small spoon to remove the seeds and inner ribs, or membranes. You can gently run water over the peppers in your sink to help remove excess seeds.
MAKE THE FILLING:
In your food processor, add the tomatoes, onion, garlic, oregano, cumin, cinnamon, and 1 tsp salt. Process until puréed, about 30 seconds.
Heat a large skillet over medium-high heat and add the puréed tomato mixture to the pan. Cook for about 5 to 8 minutes, until about half of the liquid has evaporated.
Take the pan off the heat and stir in the cooked chicken, cooked rice, cilantro, and 1½ cups of the cheese.
FINISH OFF THE DISH:
Portion the filling among the peppers, pressing their sides around the filling.
Broil the peppers on HIGH (4 inches under the heating element) until the cheese begins to melt and the tops begin to brown, about 4 minutes (keep an eye on them, don't let them burn!).
Carefully remove from the oven and top with the remaining cheese. Place under the broiler again until the cheese is completely melted and lightly browned, about 2 more minutes.
Ladle about ½ cup of the sauce into serving plates/bowls and gently place 1 stuffed pepper on top of the sauce on each plate. Serve at once.