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 sandy 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 1 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.
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