Step 1

Heat the oven to 400°F with a rack in the middle position. Coat a 9-inch deep-dish pie plate with 1 teaspoon of the oil. In a blender, combine the tomatillos, poblano, garlic, vinegar and ¾ teaspoon salt. Process until smooth, about 1 minute, scraping the sides of the blender jar as needed; you should have about 2 cups salsa verde.

Step 2

In a medium bowl, stir together the chicken, beans and 1½ cups of the tomatillo salsa. Taste and season with salt and pepper. Spread ¼ cup of the remaining salsa in the bottom of the prepared pie plate. Line the bottom with 2⅓ of the tortillas, tearing them as needed to cover the surface.

Step 3

Spread about half of the chicken-bean mixture on top of the tortillas, then top with ¼ cup of the crema. Repeat the layering with another 2⅓ tortillas, the remaining chicken mixture and another ¼ cup crema. Layer on the remaining tortillas, then pour on the remaining salsa. Drizzle with the remaining 2 tablespoons crema, followed by the remaining 1 teaspoon oil.

Step 4

Bake, uncovered, until browned at the edges, 25 to 30 minutes. Cool on a wire rack for about 5 minutes, then sprinkle with the cotija and cilantro. Cut into wedges to serve.