Meanwhile, in a separate pot, heat the milk to just under a boil. Once the mixture has browned and the milk has heated, add the milk to the roux, about one cup at a time. Whisk constantly, until very smooth, bringing it back to a boil each time. Once all of the milk has been incorporated and the mixture has come back up to a gentle boil, turn the heat to low and let cook for about 10 minutes. Stir occasionally. The sauce should nicely coat the back of a spoon. Once done, remove from the heat and season with the salt and freshly-grated nutmeg.
Besciamella sauce is widely used in many dishes, such as lasagne, soufflés, and moussaka.