In a small, heavy-bottomed saucepan, melt the butter over medium heat until it begins to gently bubble—be careful not to let it brown. Sprinkle in the flour, salt, and a dash of white pepper. Whisk continuously until the mixture forms a smooth paste, known as a roux, with no lumps remaining.

Slowly pour in the milk in a steady stream, whisking constantly to ensure a seamless blend. Continue to stir as the mixture heats, bringing it just to a boil. Once it begins to bubble, let it simmer for 1 to 2 minutes more, whisking frequently, until the sauce thickens to a creamy, silky consistency. Remove from heat and use immediately, or cover to keep warm.