Preheat the oven to 350 degrees F (175 degrees C). Spray a casserole dish with cooking spray.
Run water over the poblano peppers to remove skins and discard them; drain peppers on paper towels. Place a layer of peppers on the bottom of the prepared dish; place 1/3 of the beef mixture on top. Cover with 1 cup shredded Mexican cheese blend. Repeat layers twice more in the same order.
Bake, uncovered, in the preheated oven until golden brown on top, about 35 minutes