Spread 1 cup of the rice over the bottom of a buttered 2 1/2 quart ovenproof casserole. Top the rice with 1 cup of the flaked fish. Top fish with one of the chopped eggs.
In a skillet, cook the onions in 2 tablespoons butter over a moderate heat until they are soft.
Arranged 1/2 of the cooked onion in a layer in the casserole. Season with salt and pepper.
Add in the remaining layers; rice, haddock, chopped egg, onion and season again with salt and pepper.
In a sauce pan melt the 4 tablespoons of butter over moderately low heat. Add the flour and cook the roux, whisking, for about 3 minutes. Remove the pan from the heat, whisk in the milk, scalded, in a stream, and simmer the mixture, stirring, for 3 minutes. Stir in the nutmeg and the 1/2 teaspoons salt.
Pour the sauce over the fish mixture, making holes with a knife to let it seep down into all of the layers.
In a small bowl, combine the breadcrumbs and the remaining 3 tablespoons butter, melted and mix together.
Sprinkle the bread crumbs over the fish mixture.
Bake the pie in a preheated 350 F oven for 40 to 45 minutes, or until the crumbs are golden and the pie is bubbling.