3. Make the Béchamel
Melt the remaining 4 Tbsp butter in a small saucepan over medium heat. When the butter is foamy, drop in the flour all at once and whisk to combine. Continue to cook, whisking constantly, until the mixture has significantly lightened in color, turned very foamy, and no longer tastes like raw flour, about 1 minute.
While still whisking constantly, pour in the milk in a steady stream. Continue to cook, still whisking, until the mixture is very thick, about 1 more minute. Transfer to a large bowl.