Step 1: Prepare Your Ingredients. Finely chop the dried beef into small pieces. Toast your chosen bread until it's golden brown and slightly crispy; set aside.
Step 2: Melt Butter and Create Roux. In a medium saucepan, melt the unsalted butter over medium heat. Once melted, sprinkle in the all-purpose flour. Whisk continuously for about 2 minutes, allowing the flour to cook and turn a light golden brown. This creates your roux, which will thicken the sauce.
Step 3: Whisk in Milk. Gradually add the warm whole milk to the roux, whisking constantly to prevent lumps. Continue to whisk as the mixture comes to a gentle simmer and begins to thicken, about 3-5 minutes.
Step 4: Add Dried Beef and Seasoning. Stir in the finely chopped dried beef and the small pinch of cayenne pepper. Cook for another 2-3 minutes, stirring occasionally, until the beef is heated through and the sauce is creamy and coats the back of a spoon. Season with freshly ground black pepper to taste.
Step 5: Serve Immediately. Spoon the warm creamed chipped beef generously over the toasted bread slices. Serve hot and enjoy this classic comfort meal!