Poblano Stuffed with Mozzarella and Chicken

8 medium poblano chiles
3 medium tomatoes, chopped
1 medium white onion, chopped
2 large clove garlic, chopped
2 tsp. dried oregano, crumbled
2 tsp. ground cumin
Generous pinch ground cinnamon
1 teaspoon  salt
1 Tbs. olive oil
2  lbs shredded cooked chicken, preferably dark meat
1  cups cooked brown or white rice
2 cups grated sharp or extra-sharp white Mozzarella (about 7 oz.)
1/4 cup chopped fresh cilantro (including some tender stems)
1 Tbs. lime juice
Position an oven rack about 4 inches from the broiler and heat the broiler on high. Line a large rimmed baking sheet with foil. Slit the chiles from stem to tip and set on the baking sheet. Broil, turning every few minutes, until blackened all over, 5 to 8 minutes. Let cool slightly, peel off the skins, and cut out the seed cores, leaving the stems on. Turn the chiles inside out, flick out any remaining seeds, and turn right side out. Return the poblanos to the baking sheet.
Purée the tomatoes, onion, garlic, oregano, cumin, cinnamon, and 1/2 tsp. salt in a food processor. Heat the oil in a 12-inch skillet over medium heat. Add the purée and cook, stirring frequently, until the liquid has evaporated and the mixture looks thick and pulpy, 8 to 11 minutes. Remove the pan from the heat. Stir in the chicken and rice, and then 1 cup of the cheese, the cilantro, and the lime juice. Season to taste with salt. Divide the filling among the peppers, wrapping the sides of the peppers up and around the filling, some of which will still be exposed.