Chop the potatoes into 1 inch (3 cm) pieces and boil in salted water until slightly resistant when pierced with a knife.
Drain and bake the potatoes until very soft.
Pass the potatoes through a strainer or ricer, then mix with butter, salt, white pepper, and nutmeg over low heat until creamy.
Cool the mixture slightly, beat whole egg and egg yolks together, add to the potatoes and stir until fully combined.
Shape the potatoes as desired, chill in the fridge, then brush with melted butter and bake until browned.
