Preheat the broiler. Place tomatillos cut side down, Poblano peppers, garlic, and jalapeños on a foil-lined large baking sheet. If necessary you can use two baking sheets.Place under broiler for 8-10 minutes or until the tomatillos and peppers begin to roast and blacken.
Transfer the peppers to a gallon size bag and zip it tight (leave the tomatillos and garlic on the baking sheet for now). This allows the peppers to steam in the bag and after 5 minutes you should be able to remove the skin, stem and seeds off the peppers. Discard those.
While the peppers are steaming in the bag, add tomatillos to a blender, including all the juices. Peel garlic cloves and add them to the blender along with the peppers, cilantro, lime juice, cumin, oregano, salt, pepper and chicken broth. Blend the ingredients until smooth.
Add chicken and diced onions to slow cooker, pour green chili sauce all over the top of the chicken and stir to combine. Cover and cook on HIGH for 3 1/2 hours or LOW for 7 hours.
Before serving, remove chicken with a slotted spoon and shred with a fork. Add back to slow cooker and mix in with a spoon. Taste and adjust seasoning as necessary.