Step 1

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.

Step 2

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.

Step 3

In a medium bowl, toss together the chicken, cheese, hot sauce, 3/4 teaspoons salt and 1 teaspoon pepper; set aside.

Step 4

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.

Step 5

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.

Step 6

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.

Step 7

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.