Begin by melting the unsalted butter in a medium-sized saucepan over a low flame.

Once the butter is fully melted, gradually incorporate the all-purpose flour, whisking constantly to ensure the formation of a smooth roux.

Slowly introduce the warm whole milk to the roux, continuing to whisk diligently to prevent any lumps from forming. Subsequently, increase the heat to medium-high, ensuring constant stirring until the mixture attains a thickened consistency.

Upon achieving the desired thickness, fold in the finely chopped dried beef and incorporate the cayenne pepper. Continue to heat the mixture until the beef is adequately warmed.

To serve, ladle the creamed beef mixture over slices of toasted bread.