Broil poblanos on a metal pan 6 inches from the heat for 8 to 10 minutes, turning until skins blister. Cover in a bowl for 10 minutes, then peel, seed and chop.
Mix chicken, chopped poblanos, corn, half the cheese, cumin and salt. Stir tomatillo salsa and broth together in a separate bowl.
Brush tortillas lightly with most of the oil and warm in a skillet for about 15 seconds per side until flexible. Oil a 9-by-13-inch metal baking pan with the remaining oil and spread 1/2 cup sauce across the bottom.
Divide filling among tortillas, roll and arrange seam-side down in the pan. Spoon remaining sauce over them and scatter remaining cheese on top.
Freeze before baking: refrigerate the assembled pan promptly until cold, cover tightly with foil and a second protective wrap, label and freeze for up to 2 months.
Thaw overnight in the refrigerator, allowing 24 hours for the pan to soften throughout. Remove outer wrap and bake covered with foil at 375°F for 30 minutes.
Uncover and bake for 15 to 20 minutes more until the center reaches 165°F. Rest for 10 minutes and serve 2 enchiladas per portion.
Reheat cooked refrigerated portions covered at 350°F for 20 to 25 minutes until their centers reach 165°F.