Chop the chipped beef into small pieces and peel the pieces apart so they’re all separated. Put them in a large bowl and cover them with water and soak for 15 to 20 minutes, then drain.
While the beef is soaking, mix the evaporated milk and water in a saucepan and put over low heat.
In a separate pot, melt the butter over low heat, then add the flour. Whisk them together until smooth. Cook for a minute, then slowly pour in the hot milk mixture, whisking constantly. Cook for 3 to 4 minutes, still stirring constantly, to thicken.
Stir in the pepper and the drained chipped beef. Bring to a boil, then reduce the heat to a simmer and cook for 10 minutes.
Ladle the hot creamed beef onto some toast and serve it forth.
