Melt the butter in a medium-sized saucepan over medium heat.
Once the butter is melted and bubbling, add the flour. Cook for about two minutes, stirring constantly until a paste develops.*Do not let it brown, we are looking for a white roux.
Slowly pour in the hot milk, continuing to constantly stir, and bring to a boil. Lower the heat, still stirring, and cook for an additional 2-3 minutes until thickened.
Season with salt and pepper. Remove the pan from the heat, or use it accordingly.
Notes
Before you start making the sauce, warm the milk in a small saucepan over low heat until hot to the touch and slightly bubbly. You can also warm the milk in a microwave-safe dish in the microwave too.
Finish the sauce with a pinch of cayenne or nutmeg.