Add the butter to a large saucepan set over medium heat.
When melted, sprinkle in the flour.
Whisk constantly until there are no lumps, about a minute until the mixture has slightly darkened.
Slowly pour in the milk, whisking constantly. Keep whisking until there are no lumps.
Cook until the sauce thickens, just a couple minutes.
Add black pepper.
Stir well, and then add the dried beef.
Cook for a couple minutes to warm the beef.
Season the mixture with salt to taste, but remember that the beef is already pretty salty. If in doubt, you might wait until after the beef warms up and taste. Sometimes you won't need to add any salt at all.
When warm, spoon mixture over your bread of choice. Toasted and un-toasted white load bread works well, as do biscuits.