Bring milk to just below a simmer in a small saucepan, or use cold and heat with the roux later.

In a medium skillet over medium heat, melt the butter until foamy.

Add the flour and whisk constantly for 1 minute to cook out the raw flour taste; you’ll have a pale roux.

Slowly whisk in 1 cup of warm milk; the mixture will thicken. Add the remaining milk and whisk until silky and smooth.

Stir in the chipped beef and bring the mixture to a gentle simmer. Simmer 2–3 minutes so the beef softens and flavors meld.

Season generously with freshly ground black pepper and taste for salt. Add Dijon or Worcestershire if using.

If the gravy is too thick, thin with a splash more milk; if too thin, simmer a minute longer. Serve immediately over hot toast or biscuits.