In a 2-quart saucepan combine flour and butter. Place saucepan over medium heat.
Whisk mixture as the butter melts to break up lumps. Cook for about 30 seconds, until mixture is smooth and reaches a simmer.
Slowly add in cold milk, whisking constantly to prevent sticking and keep it smooth.
Bring mixture to a simmer. Continue to cook until the mixture thickens.
Reduce heat to low.
Crumble in blue cheese. Add black pepper. Whisk until mixture is smooth.
Increase heat to medium. Bring mixture to a simmer, whisking often. Continue to simmer until mixture thickens enough to coat the back of a wooden spoon.
Transfer mixture to a heatproof jar or container. Set aside to cool for a few minutes. Stir before using.