3 pounds pork shoulder – cut into 1.5-inch cubes
2 teaspoons kosher salt
1 teaspoons black pepper
2 tablespoons neutral oil
2 pounds tomatillos – husks removed and rinsed
2 whole poblano peppers
2 whole jalapeños
1 large white onion – halved
6 cloves garlic – unpeeled
1 cups cilantro – leaves and tender stems
1 teaspoons Mexican oregano
1 teaspoons ground cumin
3 cups chicken stock
2 whole bay leaves
2 tablespoons lime juice
cilantro – chopped (for serving)
white onion – finely chopped (for serving)
corn tortillas – warmed (for serving)
Instructions
Position an oven rack 6 inches from the broiler and heat the broiler. Line a rimmed sheet pan with foil. Arrange the tomatillos, poblano peppers, jalapeños, white onion, and garlic on the pan in a single layer.
Broil until blistered and charred in spots, 6–10 minutes, turning once halfway; set the pan aside to cool slightly so the vegetables steam and soften.
Meanwhile, pat the pork shoulder dry and season all over with the kosher salt and black pepper.
Heat the neutral oil in a heavy 5–6 quart pot or Dutch oven over medium-high. Brown the seasoned pork in 2–3 batches without crowding, 6–8 minutes per batch; transfer the browned meat to a bowl.
Slip the peels off the roasted cloves and the charred skins from the chiles as desired, remove stems and seeds from the chiles, then transfer all the roasted vegetables and any pan juices to a blender. Add the cilantro, Mexican oregano, and ground cumin; blend until very smooth (vent the lid if warm) and set the puree aside.
Pour the puree into the pot and cook, stirring and scraping up browned bits, 2–3 minutes until it simmers. Return the browned meat and any juices to the pot, add the chicken stock and bay leaves, bring to a gentle simmer, then cover partially and cook 1.5–2 hours, stirring occasionally, until the meat is fork-tender and the sauce thickly coats a spoon.
Stir in the lime juice and let the chile verde rest off heat for 5 minutes. Ladle into bowls, garnish with chopped cilantro and finely chopped white onion, and serve with warm corn tortillas.