Preheat oven to 425°. Pulse torn bagel in a food processor until coarse crumbs form. Place 1/2 cup bagel crumbs in a shallow bowl; toss with panko, cheese and pepper flakes. (Save remaining bagel crumbs for another use.)
In a microwave-safe shallow bowl, microwave butter until melted. Sprinkle chicken with salt. Dip in warm butter, then coat with crumb mixture, patting to help adhere. Place on a greased rack in a 15x10x1-in. pan.
Bake until breading is golden brown and chicken is no longer pink, 15-17 minutes.
Test Kitchen tips
One bagel will yield about 2 cups crumbs. The remaining crumbs would make a tasty topping for casseroles or used to bind meat loaves and meatballs.
For more impact, add dried minced onion and/or garlic powder to the crumb mixture.
Baking breaded foods on a rack allows the bottom to crisp up better. If you don't have a rack that will fit in your pan, you can also use a broiler pan with a rack.