In a small saucepan, combine the white wine, white wine vinegar, and shallot. Bring to a boil over medium heat, then reduce the heat to low and simmer until only 2–3 tablespoons of liquid remain.
Whisk in Butter
With the heat on low, add the cold butter a cube or two at a time, whisking constantly. Wait until each addition is almost melted before adding more. Don't let the sauce boil, or it will break.
Adding the butter too fast is what breaks it.
Season
Season with salt and white pepper to taste.
Serve
Serve right away, or keep it warm over a double boiler (just-hot water, not boiling) until you're ready to serve.
Notes
The sauce can be served with fish, shellfish, vegetables, or any other dish where you want to add a rich and creamy flavor. Enjoy!