1. Place chiles directly over the flame of a gas-stove burner on high heat. Roast chiles, turning with tongs, until blackened all over. (Alternatively, broil chiles on a baking sheet, turning, until skin has charred.) Transfer to a bowl, and cover immediately with plastic wrap. Set aside to steam, about 15 minutes. Peel chiles; discard skins. Remove stems, seeds, and ribs; cut chiles into 1-by-1/2-inch strips. Transfer to a nonreactive bowl.

2. Preheat oven to 425 degrees. Brush tortilla halves on both sides with 3 tablespoons oil. Arrange on baking sheets. Bake, rotating sheets halfway through, until tortillas begin to bubble (before becoming crunchy), 5 to 7 minutes. Set aside. Reduce oven temperature to 350 degrees.

3. Heat a large skillet over medium heat. Wash spinach, and drain but do not dry. Add spinach to skillet. Cover, and cook until spinach has wilted, about 2 minutes. Season with 1/4 teaspoon salt. Transfer to a cutting board; let cool slightly. Squeeze out liquid. Coarsely chop, and set aside.

4. Heat 2 tablespoons oil in a medium skillet over medium heat. Add onion and 1/2 teaspoon salt; cook, stirring occasionally, until translucent, about 3 minutes. Stir in chiles; cook until heated through, about 1 minute. Transfer to a bowl.

5. Heat remaining 2 tablespoons oil in same skillet. Add garlic, and cook, stirring, 30 seconds. Add beans and 1/2 teaspoon salt; cook, mashing slightly with the back of a wooden spoon, 2 minutes. Transfer to a bowl; set aside.

6. Line bottom of a 10 1/4-inch-round, 2 1/2- to 3-inch-deep baking dish with 12 tortilla halves, overlapping slightly. Layer with chile mixture, half the bean mixture, and half the crema. Spread 3/4 cup salsa over top. Sprinkle with 1/2 cup cheese. Repeat for second layer, using spinach instead of the chiles. Top with remaining tortillas, 3/4 cup salsa, and 1/2 cup cheese.

7. Bake until heated through, 45 minutes to 1 hour; cover with foil for last 15 minutes if browning too quickly or becoming too dry. Let stand 15 minutes before serving. Serve with more salsa and crema.