Warm the milk. In a small saucepan, heat the 2 cups of milk until warm, but not boiling.
While the milk is heating, melt the butter in another saucepan over medium heat. When the butter is fully melted and bubbling, slowly add in the flour while stirring with a wooden spoon or whisking with a whisk. Keep stirring until the butter and flour mixture forms a golden paste, about 3 minutes. The mixture will smell nutty as the flour cooks a bit. This recipe calls for a light roux, so the color should be light golden, and should not turn dark brown.
Add the milk. When the roux is ready, slowly pour in the warm milk a 1/4 cup at a time while whisking vigorously and constantly to ensure the sauce is lump-free.
Bring the sauce to a simmer and reduce the medium heat to medium-low heat. Continue simmering the sauce for 10 to 15 minutes, or until it thickens. The sauce is ready when it coats the back of a wooden spoon.
Stir in the salt, pepper and pinch of nutmeg. Serve or use immediately.
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