Heat large saucepan over medium heat. When pan is warm, add red wine vinegar, white wine, shallots, 1 tablespoon tarragon, pepper, and salt. Stir to incorporate and bring mixture to boil.
Let mixture boil until reduced to approximately ¼ cup total, including shallots and herbs. Approximately 2 tablespoons of liquid should remain.
When mixture is reduced, pour mixture through strainer and into blender. Discard strained aromatics. Let mixture sit in blender, uncovered, until completely cool.
While mixture cools, return saucepan to stove and reduce heat to very low. Add egg yolks and whisk until combined and thickened, then add 1 tablespoon cold butter and whisk to incorporate. Mixture should remain thick.
Add additional 1 tablespoon cold butter and remaining 2 tablespoons tarragon to saucepan. Whisk until incorporated, then transfer mixture to blender. Secure lid on blender and remove center cap. Let egg yolk mixture cool slightly.
While egg yolk mixture cools, melt remaining 12 tablespoons (¾ cup) butter in microwave. Microwave butter in 15 to 30 seconds increments, stirring between each, until butter is just melted, not bubbling or boiling.
Once egg yolk mixture has cooled, cover hole in blender lid with dish towel to prevent splattering, and blend to combine mixtures.
Drop by drop, pour melted butter into blender. Continue blending and adding butter until melted butter is incorporated and mixture has thickened. Transfer sauce to serving dish or drizzle over food and serve immediately.