Heat the oven to 190 C / 375 F and lightly grease a 23 x 33 cm / 9 x 13-inch baking dish. Pat the chicken dry and toss it with the salt and pepper. Drain and rinse the beans, and pat the thawed corn dry.
Heat the olive oil in a 30 cm / 12-inch skillet over medium-high heat. Sear the chicken in two batches, 3 to 4 minutes per batch, turning once, until browned outside but not cooked through. Move each batch to a bowl.
Lower the heat to medium and add the onion to the same skillet. Cook 4 to 5 minutes until soft, then stir in the garlic, cumin, oregano and chili powder for 30 seconds until fragrant. Sprinkle in the flour and stir for 1 minute.
Pour in the broth, scraping up the browned bits, and simmer 2 to 3 minutes until it coats the back of a spoon. Take the skillet off the heat and wait 1 minute. Stir in the Greek yogurt, then the green chiles, lime juice, beans, corn, chicken and half the cheese. Don't let the sauce boil again or the yogurt turns grainy.
Arrange half the tortilla pieces in a single overlapping layer in the baking dish. Spoon in half the filling, add the remaining tortillas, then the remaining filling. Scatter the rest of the cheese over the top.
Cover tightly with foil and bake for 20 minutes. Remove the foil and bake 15 minutes more, until the edges bubble, the cheese is spotted golden and the center reads 165 F / 74 C.
Rest the casserole for 10 minutes so the layers set. Cut into six squares and top with the cilantro.