Toss the pork with 2 tablespoons salt in a large bowl. Set aside at room temperature for 1 hour.
Preheat oven to broil.
Roast the poblano, cubanelle or anaheim peppers watching carefully and turning when charred. If you have a gas burner place peppers directly over the flame, turning occasionally until deeply browned on all sides. Place roasted peppers in a bowl, cover with plastic wrap or baking sheet and let steam for 10-15 minutes.
Peel peppers under cool running water, discarding seeds and stems. Pat dry with paper towel, then rough chop. Set aside.
With the oven still on, toss tomatillo, garlic and jalapeno with 1 tbsp olive oil and 1 tsp salt Transfer to a foil lined baking sheet and broil, turning once halfway through cooking until charred and just softened about 10 minutes.
Remove from oven, let cool slightly then add to food processor with juices. Add peeled peppers, half the cilantro and pulse the mixture until roughly pureed. Season with salt and pepper to taste.
Preheat oven to 225F. In a Dutch oven heat 2 tbsp oil until smoking. Add half of the pork and cook, without moving it, until well browned, about 3 minutes. Stir and continue cooking, until well browned on all sides. Add remaining pork and onion and cook stirring regularly until onions are softened, another 4 minutes. Sprinkle in cumin and cook another 1-2 minutes.
Add 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- 4 hours.
Return the pot to the stove top and skim off any fat. Adjust liquid to be thicker or thinner by adding boiling water or boiling it down a little to reduce. Stir in remaining cilantro and season to taste with salt.
Serve with crusty bread or warm tortillas and fresh toppers. The author advises this recipe is better once chilled in the refrigerator overnight and reheated the next day. We think he's right.