Broil poblanos on metal pan 6 inches from heat 8 to 10 minutes, turning until blistered. Cover in bowl 10 minutes; peel, seed, and chop.
Mix chicken, poblanos, corn, half cheese, cumin, and salt. Separately stir salsa and broth together.
Lightly brush tortillas with most oil; warm in skillet about 15 seconds per side until flexible. Oil 9-by-13-inch metal pan with remaining oil; spread 1/2 cup sauce over bottom.
Divide filling among tortillas; roll and arrange seam-side down. Cover with remaining sauce and cheese.
Before baking, promptly refrigerate assembled pan until cold. Cover tightly with foil and second protective wrap; label and freeze up to 2 months.
Thaw overnight in refrigerator, allowing 24 hours to soften throughout. Remove outer wrap; bake foil-covered at 375°F for 30 minutes.
Uncover; bake 15 to 20 minutes more to 165°F in center. Rest 10 minutes; serve 2 enchiladas per portion.
Reheat refrigerated cooked portions covered at 350°F for 20 to 25 minutes to 165°F in centers.