Melt the butter in a large skillet over medium heat and cook the rinsed beef for 2 minutes until the edges curl slightly.
Sprinkle in the flour and stir for 1 minute until no dry patches remain.
Whisk in the warm milk a cup at a time and simmer for 4 to 5 minutes until the gravy coats the back of a spoon.
Stir in the pepper and Worcestershire, taste, and add no salt unless the rinsed beef was unusually mild.
Toast the bread until crisp at the edges, spoon the creamed beef over 2 slices per serving, and scatter exactly 1 teaspoon parsley over each plate.