Place carrots into a saucepan and cover with water; bring to a boil. Reduce heat to medium-low and simmer until just soft, 6 to 8 minutes. Drain, reserving 1/4 cup of cooking liquid.
Mix onion, horseradish, mayonnaise, Parmesan cheese, and reserved 1/4 cup liquid in a bowl; toss horseradish mixture with carrots. Transfer carrot mixture to a shallow baking pan. Season with salt and black pepper. Sprinkle panko bread crumbs over carrots.
Bake in the preheated oven until bread crumbs are lightly browned, about 20 minutes.
