Preheat the oven to 425 degrees F. Lightly coat a 9x13-inch baking dish with nonstick spray.

In a large skillet, heat the oil over medium-high heat. Add the onion, red bell pepper, poblano pepper, chili powder, cumin, and salt. Cook, stirring frequently, until the vegetables have softened and are beginning to brown, about 6 minutes, reducing the heat if the vegetables begin to burn. Transfer to a large mixing bowl. Add the chicken, corn, 1/4 cup cheese, Greek yogurt, and 1/3 cup enchilada sauce. Stir to combine. Set aside.

With a vegetable peeler or mandoline slicer, slice the zucchini lengthwise into thin strips that are about 1/8 inch thick. You want the zucchini to be thin enough to roll easily, but not so thin that it tears. Test the first few slices to make sure you are happy with how they are coming out. Discard any uneven and broken pieces. You will have about 48 slices total.

Spread 1/4 cup of the remaining enchilada sauce on the bottom of the dish. On a large clean work surface, arrange 3 strips of the zucchini next to each other, overlapping the edges by about 1/4 inch (what you are doing here is making 1 big faux tortilla). Place a heaping 2 tablespoons of the chicken filling across the middle of the zucchini strips.

Starting at the short ends (not the sides), gently roll the zucchini strips around the filling like a sleeping bag. Carefully place the roll seam-side down in the prepared dish. Repeat with the remaining zucchini strips and filling. (You should have 16 enchiladas.) Top the zucchini rolls with the remaining enchilada sauce and 3/4 cup cheese.

Bake the enchiladas until the sauce is bubbling and the cheese is melted, 20 to 25 minutes. Serve hot, with any and all desired toppings.