Béchamel - also called white sauce or white gravy -is a cooked mixture of butter, flour, and milk with salt and pepper. This is most commonly used as a base for cheese sauces.
Melt the butter in a large saucepan over medium heat. Add the flour and whisk into the melted butter until smooth.
Cook, stirring, until the butter mixture turns golden brown, around 5-7 minutes.
Slowly whisk in one cup of the milk, adding very slowly to avoid clumps, whisking continuously. Once combined, whisk in the other cups of milk, slowly, until all of the milk is whisked into the mixture.
Bring to a low simmer, stirring, then reduce the heat to medium-low. Continue simmering for another 10 minutes, stirring, until the mixture is smooth and the flour no longer is gritty in the mixture.
Remove from the heat and season with salt and pepper
Notes
If you can, warm the milk in a microwave-safe liquid measuring cup in your microwave for one minute to take the chill off. It will mix into the sauce easier, preventing lumps