Heat the milk in a pot over medium heat until it just starts to bubble, but is not boiling, 3 to 4 minutes. Remove from heat.
Heat the butter over medium heat in a separate, heavy-bottomed pot. When the butter has melted, add the flour and whisk constantly until the mixture turns light brown, about 3 minutes. Remove from heat.
Slowly pour the warm milk, about 1 cup at a time, into the butter-flour mixture, whisking constantly. It will get very thick when you first add the milk, and thinner as you slowly pour in the entire 3 cups. This is normal.
Once all the milk has been added, set the pot back over medium-high heat, and continue to whisk constantly. In the next 2 to 3 minutes the sauce should come together and become silky and thick. Use the spoon test to make sure it's ready. To do this, dip a metal spoon into the sauce -if the sauce coats the spoon and doesn't slide off like milk, you'll know it's ready. You should be able to run your finger along the spoon and have the impression remain. Add the salt.
The Bechamel Sauce is ready to use immediately and does not need to cool. Store it in the fridge for a day or two if you want to make it ahead of time -it will get a lot thicker when you put it in the fridge, so you may a little milk to thin it out a bit when it comes times to melt in the cheese. Try melting the cheese into the sauce first, and if it is too thick then add milk as needed.