Rinse the dried beef under cold running water to remove surface salt. Dab dry with absorbent paper towels, then cut into thin, narrow strips.
Place a medium-sized skillet over medium heat and add the butter. Once melted, whisk in the flour and continue stirring for about 1 minute, or until the mixture becomes smooth and starts to bubble.
Gradually pour in the warm milk, whisking constantly to ensure a lump-free sauce. Continue to stir until the mixture thickens to a creamy consistency, approximately 3 to 5 minutes.
Incorporate the prepared beef into the thickened sauce. Let it simmer gently for 2 to 3 minutes, allowing the meat to heat through evenly.
Sprinkle in the black pepper and, if desired, a pinch of cayenne for extra depth. Adjust the seasoning as needed.
Ladle the hot, creamy beef mixture generously over freshly toasted bread slices. Serve immediately while warm.