To begin, dried beef is highly salted and you really don’t want all of that in your food. Rough chop the beef, then set it in a small colander or sieve to rinse under cold water. Set aside for now.
In a large saucepan, melt the butter over medium heat. Whisk in the flour and cook for a minute until the mixture bubbles.
Whisk in the milk and heat this while continually stirring until it comes to a boil and is nice and thick.
Remove it from heat and stir in the black pepper and then stir in the chopped dried beef.