Place a pan on medium-low heat. Into the pan add the butter.
When the butter melts, add the flour. Cook it for 2-3 minutes with thorough mixing to decrease the floury taste.
Season the flour with the black pepper. Add in the milk to make the creamy sauce. Stir it becomes smooth with the preferred consistency.
After cutting the dried beef into bite-sized pieces, add it to the pan.
If the sauce is too thick, you can add more milk, ¼ cup at a time, until it reaches the desired consistency.
Serve it warm over the toast. Enjoy!