Preheat oven to 425 degrees F. Drizzle the olive oil over onion, poblano, and tomatillos on a baking sheet and roast until vegetables are soft and browned, 35–40 minutes. Let cool slightly before peeling the skin off the poblano. Transfer the mixture and any 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 with salt and pepper as needed.
Toss the chicken with the ground coriander, red pepper flakes, and ½ cup green sauce in a large bowl and season with salt and pepper .
Heat vegetable oil in a medium skillet over medium-high. 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.
Dip both sides of each tortilla in green sauce just to coat, then transfer to a baking sheet. Spread 1 cup green sauce lengthwise down the center of a 13x9" baking dish. Working one at a time, spoon ¼ cup of the chicken mixture into the center of tortilla and fold one side over filling, then continue to roll enchilada up like a burrito. Place seam side down in prepared baking dish as you go, fitting them all in. Top with the remaining green sauce and then pile on the cheese. Bake until sauce is bubbling and cheese is beginning to brown, 20–25 minutes.
While the enchiladas are baking, combine the crème fraîche and milk and season with salt.
Serve enchiladas topped with cheese, a drizzle of crema, sliced onion and cilantro.