Can I use a fat free milk to make the sauce? Should I add more butter to the roux if I do so?
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I know I've done it with 1% and 2% ... I've likely done it with skim, but I've been off milk for years and can't remember for sure if I've done it. – Joe Aug 31 '15 at 22:44
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related : http://cooking.stackexchange.com/q/9300/67 – Joe Aug 31 '15 at 22:44
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2@papin this seems to be already an answer. We prefer people to add answers in answers, not in comments, because 1) they are more likely to be read where they belong, 2) comments are ephemeral and can be deleted at any time with no reason or warning, and 3) the voting system doesn't work with comments. Don't be afraid to post a very short answer as an answer. If it's sufficient, it's even better than a wordy one. – rumtscho Sep 01 '15 at 08:47
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Yes. The important fat is the one the starch first goes into. The higher temperature reached by fats (as compared to water or milk) helps cook the flour, creating flavors. The liquid added later dilutes the mixture into a sauce. The liquid's fats are not as crucial for the sauce's thickness as the liquid's proteins.
I think of the cooked butter-flour mixture as a thickner that can be added to milk, broths, and even a saucy dish. The roux thickens way better than just a slurry of flour and a cold liquid.
Jack Lang has written a long post on Béchamel and Hollandaise and the science is summarized in chapter 4 of Vaclavik and Christian Essentials of Food Science

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