1. Heat 1 tablespoon butter in 2-quart saucepot over medium. Add shallot and sauté 2–3 minutes, stirring occasionally. Pour vinegar into pan, and add 4 sprigs tarragon; simmer until liquid has reduced to about 1 tablespoon. Strain and cool reduction.
2. Fill small saucepot halfway with water; bring to boil on high. Reduce heat to low and keep simmering. Separate eggs for yolks only (reserve egg whites for another use). Place egg yolks in a medium-sized, metal mixing bowl. Squeeze one-half lemon into bowl and whisk until smooth. Place bowl over simmering water and cook mixture, whisking continuously (if it seems as if yolks are cooking too fast, remove bowl from heat and whisk yolks to cool).
3. Add remaining 15 tablespoons softened butter to egg yolks, 1 tablespoons at a time; whisk until melted and emulsified. Sauce will seem thin at this point; keep whisking sauce in bowl over simmering water until thickened.
4. Remove bowl from heat and stir in salt, white pepper, cayenne, hot pepper sauce, and Worcestershire. Chop remaining 1 sprig tarragon; Squeeze over bowl remaining one-half lemon, and stir in chopped tarragon and tarragon reduction. Keep sauce warm until ready to serve.

Serving suggestion: Pan-Seared New York Strip