Heat the broiler and arrange the tomatillos, poblanos, jalapeño, onion and garlic on an oiled rimmed pan.
Broil 6 inches from the heat, turning once, until the vegetables have dark spots and soften, 10 to 12 minutes.
Peel the garlic and blend all the roasted vegetables with the broth, cumin and salt until mostly smooth.
Pour the green sauce into a 5-quart slow cooker and fold in the pulled pork and hominy.
Cover and cook on low until the pork has absorbed the sauce and the hominy is tender, 3 to 3 1/2 hours.
Stir in the lime juice, taste for salt and let the chile verde stand uncovered for 10 minutes.