Combine vinegar, chopped tarragon, shallots, and a tablespoon of water in a small saucepan. Simmer over low heat until the mixture is reduced to about two tablespoons.
- Strain the reduction into a heatproof bowl, discarding solids.
- Add egg yolks to the reduction and whisk until well blended.
- Place the bowl over a pot of simmering water (double boiler) and continue to whisk vigorously. Ensure the bowl does not touch the water.
- Gradually add melted butter, continuing to whisk, until the sauce thickens and doubles in volume.
- Remove from heat, season with salt and pepper, and serve immediately with steak.