Step 1
Preheat the oven to 400 degrees F (200 degrees C).
Step 2
Fill a large pot 3/4 full with water and bring to a boil. Add chicken and season with salt and black pepper. Cook until chicken is no longer pink inside about 15 minutes.
Step 3
Meanwhile bring 1 cup water to a boil in a medium-sized pot. Add tomatillos serrano pepper and garlic. Boil for 12 minutes.
Step 4
Heat a cast iron skillet over medium heat. Place poblano peppers in a resealable plastic bag and add 1 tablespoon oil. Toss to coat. Transfer peppers to the hot skillet and roast until dark brown on all sides about 5 minutes. Return roasted peppers to the resealable bag and seal. Set aside to steam for 10 minutes. Take out peppers from the bag; remove and discard skins and stems.
Step 5
Use a slotted spoon to transfer tomatillos serrano peppers garlic and 1/2 cup of the cooking liquid to a blender. Add onion cilantro lime juice roasted poblano peppers salt and pepper to the blender. Liquefy into a smooth sauce.
Step 6
Remove chicken from the water in the pot and shred using a fork.
Step 7
Heat 1/2 cup oil in a skillet over medium heat. Fry tortillas in the hot oil until softened about 5 seconds on each side. Transfer to a plate lined with paper towels to absorb excess oil.
Step 8
Pour 1/2 the sauce from the blender into the bottom of a long glass baking pan. Roll a portion of chicken mixture and some shredded queso cheese on a tortilla roll up and place in the pan. Repeat with remaining tortillas chicken mixture and queso cheese. Cover enchiladas with remaining sauce. Use a spoon to add crema in a zigzag design on top. Top everything with remaining queso cheese.
Step 9
Bake in the preheated oven until cheese starts to brown about 20 minutes.