Arrange an oven rack 4 inches underneath oven broiler and preheat broiler.
Place poblanos, tomatillos, serranos, garlic and onion on a baking sheet lined with foil or silicone baking mat; place pan under broiler. Use tongs to turn vegetables as needed until they are charred on all sides, about 10 minutes. Let cool for about 10 minutes, then peel and discard skins from poblanos.
Transfer roasted tomatillos, chiles, garlic and onion to a blender with cilantro, sour cream, cumin, garlic, chicken broth, salt and pepper. Purée until smooth. Set aside.
Heat oil in skillet over medium high heat. Working in batches, fry tortillas in oil until pliable, about 1 minute, turning with tongs or fork. Transfer tortillas to plate and cover with towel.
Preheat oven to 375°F.
Place shredded chicken in bowl with 1 cup of the enchilada sauce and stir to combine. Divide chicken evenly over each tortilla, and roll each tightly around chicken. Pour 1 cup enchilada sauce in the bottom of a 9″ x 13″ baking dish, and place rolled tortillas seam side down in dish, creating one row down the center of the dish. Pour remaining sauce over enchiladas, then cover with layer of shredded cheese.
Place baking dish in preheated oven uncovered, and bake for 25 minutes. Remove from oven, and allow white chicken enchiladas to cool for 10 minutes. Serve with more sauce poured on top.