Mix all the ingredients together and sauté over medium high heat until golden brown, about 8 minutes.
At the restaurant, the hash is placed on a plate, topped with two poached eggs, bechamel sauce is ladled on, and it is served with two slices of toast.
If you wish to use the bechamel sauce:
In a medium saucepan, heat the butter over medium-low heat until melted. Add the flour and stir until smooth. Over medium heat, cook until the mixture turns a light, golden color, about 6 to 7 minutes.
Meanwhile, heat the milk in a separate pan until just about to boil. Add the hot milk to the butter mixture, a cup at a time, whisking continuously until very smooth. Bring to a boil. Cook 10 minutes, stirring constantly, then remove from heat. Season with salt and nutmeg, and set aside until ready to use. Makes about 1 1/2 cups. Use amount of sauce to taste.