Char the poblano peppers all over by placing the peppers on stovetop burners or under a hot broiler until black, turning frequently. Place the charred peppers in a bowl and cover with plastic wrap to steam them as they cool. Rub the skins off the poblanos and jalapenos with paper towel or peel by hand, then seed the peppers and chop.
Meanwhile, heat the extra-virgin olive oil in a medium-size Dutch oven over medium heat, add the onions and sweat 10 minutes then add the garlic and tomatillos and cook 10 minutes more; season with salt and pepper. Place the cooked onion-tomatillo mixture in a food processor with cilantro, cumin, honey, and puree. Add the puree back to the Dutch oven, then stir in the chopped peppers and chicken stock. Bring the mixture to a boil, reduce the heat to low for the flavors to combine. Slice and finely chop the cooked pork and stir into the chili. When the soup returns to a bubble, turn off the stove, cool completely and store for make-ahead meal.
To reheat the chili: Place in covered pot over medium heat and cook until the pork comes to a bubble, stir in the juice of 1 lime and turn off the heat. Slice the remaining lime into wedges and serve alongside the chili.
For the cheesy polenta: In medium saucepan, bring the chicken stock and milk to a boil. Whisk in the polenta, stirring until the polenta just pulls from the side of the pot. Stir in the Manchego cheese and serve warm.