Using a sharp knife, roughly slice the thin sheets of dried beef into small, bite-sized ribbons. If using traditional jarred dried beef, quickly rinse the meat under cold water and pat dry with paper towels to draw off the aggressive curing surface sodium before chopping.
Melt the unsalted butter in a medium skillet over medium-low heat until it becomes completely fluid and foamy.
Sprinkle the all-purpose flour directly over the bubbling butter, whisking continuously to form a smooth paste.
Cook the butter and flour mixture together for 90 to 120 seconds, stirring frequently. Pro Tip: You are creating a classic blond roux. Letting the paste cook slightly without darkening is crucial—it toasts the starch cells to completely remove the raw, chalky flour taste while keeping the gravy a stark, beautiful cream color.
Pour the whole milk into the skillet in a slow, steady stream while whisking vigorously. Continue cooking over medium-low heat for 3 to 4 minutes until the starches fully swell and the liquid expands into a thick, glossy, velvet sauce.
Season the smooth white base with the black pepper and a minimal 1/4 teaspoon of kosher salt. Stir to combine.
Drop the chopped chipped beef ribbons directly into the simmering cream sauce. Stir gently for 1 to 2 minutes. The heat will cause the tightly packed meat fibers to uncurl and separate from one another, suspending them evenly throughout the hot gravy. Taste the sauce now and add more salt only if desired.
Drop your bread slices into the toaster and run them for a double cycle until they are a deep, dark golden brown. Lay the hard toast flat on a serving plate and smother the surface immediately with the hot creamed beef. Serve right away.