2 cups shredded Chihuahua-style white cheese, divided
1 bunch cilantro
8 flour tortillas
½ cup sour cream
In a small bowl, combine juice of half of one lime and sliced red onion with a pinch of salt. Set aside.
Heat broiler and move oven rack to top level. Toss poblanos, jalapeño, yellow onion, garlic, and tomatillos in oil. Add a pinch of salt and transfer to a rimmed baking sheet. Broil vegetables until browned, rotating tray often, about 12 minutes. Remove from oven and let cool. Return oven rack to middle level and turn oven to 425 F.
Meanwhile, combine chicken, green onions, and 1 cup cheese. Set aside.
When vegetables have cooled slightly, use a knife to scrape skin off poblanos and jalapeño. Remove skin from onion and garlic. Add all the vegetables to a blender along with the whole bunch of cilantro (stems and all, reserving a few sprigs for garnish, if desired) and juice of remaining limes. Blend salsa until smooth.
Add ½ cup salsa to a 9x13-inch baking dish and place the rest in a medium bowl. Lightly warm the tortillas in a microwave or over a gas burner. Working one at a time, dip a tortilla into the sauce, fill with about ½ cup of the chicken mixture, roll it up, and place it seam side down in the baking dish. Repeat with remaining tortillas.
Top rolled tortillas with any remaining salsa. Sprinkle with remaining 1 cup shredded cheese and bake until cheese begins to brown, 12 to 15 minutes. Remove from oven and let cool slightly.
Thin sour cream with about a tablespoon of water. Drizzle over the enchiladas, then top with marinated red onion and reserved sprigs of cilantro, if using.