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Step 1
In a large skillet (or high-sided braiser): melt the butter over low heat. Sprinkle the flour on top; mix well with a wooden spoon. Cook, stirring frequently, for 30 seconds to 1 minute to make a light roux. It will look like thick paste. Do not burn.
Step 2
Take the pan off the heat. Add 1/2 cup milk and whisk thoroughly to break up the lumps. Keep whisking until the mixture looks creamy. Slowly add the rest of the milk, whisking continuously as you pour.
Step 3
Return the pan to the heat. Adjust to medium-low. Cook the sauce, whisking often, until it has thickened to the consistency of runny sour cream (it will thicken more as it cools). This should take about 12 minutes or more depending on the size of your pan. Season with salt to taste.
Step 4
When ready, the sauce should coat the back of a wooden spoon. Note: If not using the béchamel sauce right away, if will form a skin on the surface. See storage tips below.