Broil poblanos on sheet 10 to 12 minutes, turning, until blistered. Cover in bowl 10 minutes; peel, seed, slice into strips, and pat dry.
Heat oven to 350°F; oil 9-by-13-inch dish. Layer half tortilla strips, beans, corn, peppers, and cheese; repeat remaining halves.
Whisk eggs, milk, cumin, and salt; evenly pour over. Gently press tortillas into custard.
Foil-cover; bake 30 minutes. Uncover, add crushed chips, and bake 15 to 20 minutes more to 160°F in center.
Rest 10 minutes so layers hold when cut.