Heat the broiler to 500°F. Line a rimmed baking sheet with foil. Arrange the peppers in a single layer on the prepared baking sheet. Spritz with nonstick spray. Place the baking tray in the upper third of your oven, and roast for about 10 minutes, until the chile peppers start to blister and blacken.
Remove to a bowl and cover so that the peppers will sweat, making the skins easier to remove. Remove and discard the skins and seeds. (You can rinse under cold water in the sink, but that will also remove flavor; try to use your hands and a paper towel.) Coarsely chop the peppers and set aside.
Reduce the oven temperature to 400°F. Heat a large deep skillet or shallow saucepan over medium-high heat. Spray with nonstick spray. Add onion and cook until clear and translucent, about 3 minutes. Add turkey, ground cumin, ground coriander, and garlic. Stir to combine. Cook until the meat is no longer pink, about 5 minutes.
Add corn and reserved chopped fresh peppers or drained canned peppers; stir to combine. Season with salt and pepper.
Lay 4 tortillas in the bottom of a 9-inch-by-13-inch casserole dish. Top with half of the turkey-corn mixture. Dollop in half the drained beans. Top with the remaining tortillas, then the remaining turkey-corn mixture. Repeat with the remaining beans. Sprinkle cheese on top.
Bake until heated through, brown and bubbly, 30 - 45 minutes. Remove to a rack or the stovetop to let cool slightly before serving.