Instead of chopped onion, Shirley recommends using it grated, which imparts the desired flavor but omits the chunks that are unappealing to some palates.
Scrape carrots and cut on diagonal, making slices about ¼-inch thick. Cook in salted water until tender but still crisp. Drain, reserving ¼ cup cooking liquid. Mix onion, horseradish, mayonnaise, salt, pepper, and carrot liquid; combine with carrots in a buttered casserole. Mix the bread crumbs with the melted butter and spread over the carrots. Bake at 375 degrees F for 15 to 20 minutes or until bubbly.