Arrange the tomatillos, poblanos, jalapeño, onion and garlic on a rimmed sheet pan and broil 5 inches from the heat for 8 to 10 minutes until blistered and browned in spots.
Blend the broiled vegetables with the broth, cumin, oregano and 1 teaspoon of the salt until mostly smooth.
Place the pork in a 6-quart crockpot, pour over the green sauce, and add the remaining salt.
Cover and cook on low for 7 hours, add the pinto beans, and cook for 1 more hour until the pork is fork-tender and reaches at least 145°F.
Stir in the lime juice and break only the largest pork cubes, leaving plenty of distinct pieces in the sauce.