Heat the butter in a saucepan over medium-high heat until melted. Add the flour and stir to combine. Cook, stirring constantly, until foaming. Add the beef stock and stir to combine. Reduce heat and let simmer until thick enough to coat a spoon. You should have about 1 1/2 cups.

In a second saucepan combine the tarragon vinegar, white wine, shallot, and tarragon until reduced by half.

Add to the simmering gravy and stir to combine. Add cayenne pepper and dry mustard. Simmer until thick enough to coat a spoon, 3 to 5 minutes. Strain through a fine mesh strainer. Taste and adjust for seasoning with salt and pepper and keep warm.