Step 1

Preheat oven to 425°. Drizzle olive oil over onion, poblano chile, and tomatillos on a rimmed baking sheet and roast until vegetables are soft and browned, 35–40 minutes. Let cool slightly, then slip off and discard poblano skin. Transfer onion mixture and any accumulated juices to a blender. Add serrano chiles, garlic, chicken stock, cilantro, and lime juice and purée until smooth. Transfer to a large bowl, then season green sauce with salt.

Step 2

Preheat oven to 425°. Toss chicken with coriander, chile de árbol, and ½ cup green sauce in a large bowl; season with salt.

Step 3

Heat vegetable oil in a medium skillet over medium-high until oil bubbles immediately when edge of tortilla touches the surface. Working one at a time, fry tortilla, turning once, until just starting to brown and crisp, about 10 seconds per side. Transfer tortilla to paper towels to drain. Repeat with remaining tortillas.

Step 4

Dip both sides of each tortilla in green sauce just to coat, then transfer to a rimmed baking sheet. Spread 1 cup green sauce lengthwise down the center of a 13x9" baking dish. Working one at a time, spread ¼ cup chicken mixture down the center of tortilla and fold one side over filling, then continue to roll enchilada onto itself. Place seam side down in prepared baking dish as you go (enchiladas should be nestled right up against each other). Top with 10 oz. cheese and remaining green sauce. Bake until sauce is bubbling and cheese is beginning to brown, 20–25 minutes. Let sit 10 minutes.

Step 5

Meanwhile, combine crème fraîche and milk; season with salt.

Step 6

Serve enchiladas topped with cheese, a drizzle of crema, and sliced onion.