• 3 tablespoons extra-virgin olive oil, divided
• 3 medium poblano chilies (about 12 ounces), stemmed, seeded and chopped
• 1 pound tomatillos, husked, cored and chopped
• 1 medium white onion, chopped
• 6 medium garlic cloves, peeled
• 1 tablespoon ground cumin
• ½ cup low-sodium chicken broth or water
• 1 cup lightly packed cilantro leaves and stems
• Kosher salt and ground black pepper
• 1½ cups finely chopped cooked chicken (see note)
• 6 ounces whole-milk mozzarella cheese, shredded (1½ cups)
• 2 tablespoons hot sauce (see note)
• 8 6-inch corn tortillas
• Lime wedges, to serve
Heat the oven to 475°F with a rack in the middle position. In a large pot over medium-high, combine 1 tablespoon of the oil, the poblanos, tomatillos, onion and garlic. Cook, stirring occasionally, until the vegetables are well-browned and beginning to soften, 5 to 8 minutes. Stir in the cumin and cook until fragrant, about 30 seconds. Add the broth and cook, stirring occasionally, until the vegetables have softened, about 5 minutes. Remove from the heat and let cool for 5 minutes.
Transfer the mixture to a food processor and process until smooth, about 1 minute. Add the cilantro and continue to process until smooth, about 1 minute. Taste and season with salt and pepper. Spread 1 cup of the sauce in the bottom of a 13-by-9-inch baking dish; set aside.
In a medium bowl, toss together the chicken, cheese, hot sauce, 1½ teaspoons salt and 1 teaspoon pepper; set aside.
Brush both sides of the tortillas with the remaining 2 tablespoons oil, then arrange them on a rimmed baking sheet (its fine to overlap them slightly). Cover tightly with foil and warm in the oven just until soft and pliable, about 3 minutes.
Uncover the tortillas; reserve the foil. Lay the tortillas out on a large cutting board or clean counter. Divide the chicken mixture evenly among the tortillas (about 3 heaping tablespoons each), arranging and pressing the filling in a line along the bottom edge of each tortilla.
Working one at a time, roll up the tortillas to enclose the filling and place seam side down in a tight row down the center of the prepared baking dish. Spoon ½ cup of the sauce over the enchiladas. Cover tightly with the reserved foil and bake until the cheese begins to melt out of the ends, about 15 minutes.
Uncover and spread ½ cup of the remaining sauce over the enchiladas. Re-cover and let stand for 5 minutes. Serve with lime wedges and the remaining sauce.