In a slow cooker, combine tomatillos, poblanos, onion, serrano or jalapeño, ½ cup fresh cilantro, oil, garlic, 1 teaspoon kosher salt, oregano, pepper, and coriander, and stir to combine.
Season chicken with remaining 1 teaspoon kosher salt and nestle into slow cooker, tossing to coat in the mixture. Cover and cook on low setting, stirring mixture about halfway through, until chicken is pull-apart tender, 4 to 5 hours.
Using tongs or two forks and working inside the slow-cooker crock, shred chicken into bite-size pieces. Stir in remaining ½ cup cilantro and lime juice. Stir to combine mixture and season to taste with salt, pepper, and lime juice. Serve with warm tortillas and your favorite taco toppings.
