Bring the milk to simmer in a saucepan, then keep the milk on low heat.
2 cups whole milk
Make a roux: In a separate sauce pan, melt the butter over medium-low heat. Add the flour and whisk vigorously for about a minute until thick and smooth.
6 tbsp flour, 3.5 tbsp butter
Add a ladle of the warm milk to the roux a little at a time, whisking vigorously until smooth before adding more milk. When all of the milk has been incorporated, continue to simmer the sauce (whisking regularly) for about 5 minutes or until the béchamel coats the back of a spoon.