Toss the pork with 2 tablespoons salt in a large bowl until thoroughly coated. Set aside at room temperature for 1 hour.

Meanwhile, roast the poblano and cubanelle peppers by placing them directly over the flame of a gas burner, turning occasionally, until charred on all surfaces, about 10 minutes. Or, if you don't have a burner, you can achieve similar results under the broiler or on an outdoor grill. Place the roasted peppers in a bowl, cover with a large plate, and let steam for 5 minutes.

Peel the peppers under cool running water, discard the seeds and stems, and pat dry, then roughly chop. Transfer to a food processor.

Preheat the broiler to high. Toss the tomatillos, garlic, and jalapeños with 1 tablespoon of the vegetable oil and 1 teaspoon salt. Transfer to a rimmed baking sheet lined with foil and broil, turning once halfway through cooking, until charred, blistered, and just softened, about 10 minutes. Transfer to the food processor, along with any juices. Add half of the cilantro and pulse the mixture until roughly pureed but not smooth, about 8 to 10 short pulses. Season to taste with salt and pepper.

Adjust an oven rack to the middle position and preheat the oven to 225°F. Heat the remaining 2 tablespoons oil in large Dutch oven over high heat until smoking. Add half of the pork and cook, without moving it, until well browned, about 3 minutes. Stir and continue cooking, stirring occasionally, until well browned on all sides. Add the remaining pork and the onion and cook, stirring frequently and scraping up any browned bits from the bottom of the pot, until the onions are softened, about 4 minutes. Add the cumin and cook, stirring until fragrant, about 1 minute.

Add the chicken stock and pureed chile mixture and stir to combine. Bring to a boil, cover, and transfer to the oven, leaving the lid slightly ajar. Cook until the pork shreds easily with a fork, about 3 hours.

Return the pot to the stovetop and skim off and discard any fat. Adjust the liquid to the desired consistency by adding water or boiling to reduce. Stir in the remaining cilantro and season to taste with salt. Serve or let the chili cool and refrigerate overnight, then reheat to serve. Serve with some or all of the suggested garnishes, along with warm tortillas.