In a saucepan, cook carrots just until crisp-tender; drain, reserving quarter cup cooking liquid. Place carrots in a 1- half quart baking dish. Combine mayonnaise, onion, horseradish and reserved cooking liquid. Spread evenly over carrots. Sprinkle with cheese; top with bread crumbs.
Bake, uncovered, at 180ºC or 30 minutes.