In a medium saucepan over low heat, melt the butter. Add flour, pepper, and salt, then whisk to combine. Bring just to a simmer, add 1/2 cup milk, and whisk until fully incorporated.

Increase the heat to medium. Stir constantly until the mixture begins to thicken. Gradually add the remaining milk, 1/4 cup at a time, whisking thoroughly until gravy is smooth and thickened slightly.

Adjust seasoning to taste and serve hot.