In this dish, Anaheim chile peppers make envelopes for Mexican-style caramelized pork.
Place pork in a large, heavy pot. Sprinkle with salt. Add water to cover. Bring to a boil. Reduce to a simmer. Cook, stirring occasionally, until pork is brown, about 1 1/2 hours (when water has evaporated, pork will brown in its fat). Set aside.
Preheat oven to 375 degrees. Place chiles directly over the flame of a gas-stove burner on high heat. Roast, turning with tongs, until blackened all over. (Alternatively, broil chiles on a baking sheet, turning, until skin has charred.) Transfer chiles to a large bowl, and cover immediately with plastic wrap. Set aside to steam, about 15 minutes. Peel chiles; discard skins. With stems intact, slit each chile lengthwise; carefully remove seeds and veins. Place, slit side up, on a baking sheet.
Spread 2 tablespoons cheese in bottom of each chile, then fill with 1/3 cup pork. Sprinkle chiles with remaining 2 cups cheese. Spoon 1 tablespoon tomatillo sauce over top of each chile. Bake 15 minutes. Garnish with cilantro; serve with tortillas and remaining tomatillo sauce.