Fry chopped onions in 1/4 cup butter, when soft add 1/4 cup flour and pepper to taste. Brown slightly and put in a bowl.
Bring enough water to cover fish to a boil then add fish. Boil 2 minutes. Remove fish from water and save fish broth.
Dry pan and melt 1/4 cup butter, add 1/4 cup flour and cook for 2 minutes. Add 1 cup milk, 1/2 cup fish broth, and horseradish and cook for 1 more minute. Stir in fish, onions, and most of cheese. Top with remaining cheese.
Bake in the preheated oven until browned slightly, aobut 20 minutes.