1) Char chiles directly over gas flame or in broiler until blackened all over. Enclose in plastic bag; let stand 10 minutes. Peel and seed, then cut into 2×1/2-inch strips.

2. Preheat oven to 375°F.

3. Toss cut tortillas in a large bowl with 2-3 tablespoons oil. Spread out onto two baking sheets and bake until crisp and lightly brown.

4. Spread 1/2 cup salsa over bottom of 8x8x2-inch glass baking dish. Arrange 1/3 of the crisp tortillas over salsa, covering bottom of dish completely, overlapping slightly, and extending about an inch up sides of dish.

5) Scatter 1.5 cups chicken over tortillas, then half of poblano strips. Spoon 1 1/2 cups salsa over, spreading evenly. Spoon 1/4 cup crema over in small dollops. Cover with tortillas, overlapping slightly. Layer with remaining 1.5 cups chicken, remaining poblanos,  salsa, and 1/4 cup crema. Cover with remaining tortillas, then 1 cup salsa, and remaining 1/4 cup crema. Sprinkle with cheese.

6. Bake until bubbling and cheese is lightly browned, about 35 minutes. Sprinkle with cilantro. Spoon pickled red onions alongside; serve.