Make the reduction: In a small, heavy-bottomed, nonreactive saucepan, combine the chopped shallots, white wine vinegar, and white wine. Bring to a boil, then reduce the heat to medium. Simmer uncovered until the liquid has reduced to about 2 tablespoons.

Add the cream: Whisk in the whipping cream. Reduce the heat to low and simmer, whisking occasionally, until the mixture has reduced to about 3 tablespoons. At this point, the reduction can be cooled, covered, and refrigerated for up to 1 day.

Emulsify the butter: If the reduction has been refrigerated, gently warm it and season lightly with salt and pepper. Keep the heat on low. Add one cube of softened butter and whisk constantly. When the butter is nearly incorporated, add another cube and continue whisking. Repeat, adding the butter one cube at a time.

Control the temperature: The sauce should remain pleasantly warm and gradually become thick and creamy. If it becomes too hot and melted butter begins to separate from the sauce, immediately remove the pan from the heat and whisk vigorously. Add the next 3–4 cubes of butter off the heat, continuing to whisk. Once the sauce has cooled back to a warm temperature, return it to low heat and continue adding the remaining butter.

Finish: Remove the saucepan from the heat as soon as the last cube of butter is incorporated. Strain the sauce if desired. Taste and adjust the salt and pepper.

Keep warm and serve: Serve the Beurre Blanc as soon as possible. If necessary, keep it warm over a pan of warm water, whisking frequently and maintaining a consistent temperature to prevent separation. It can also be kept warm in a thermos.