In a 2 to 3-quart pan over high heat, boil vinegar, vermouth, shallots, and tarragon until reduced to ¼ cup, 5 to 8 minutes. Let stand at room temperature up to 2 hours.
Just before serving, set pan over high heat, add butter, and stir constantly until it’s melted and bubbling, 2 to 3 minutes. Serve warm. (Yields about 1 cup)
Serve this herby butter sauce with a mild fish like sole.