Place vinegar in a non-aluminum pan and add shallots, dried tarragon and peppercorns. Reduce by ¾. Remove from heat and cool slightly.
Transfer reduction to a round bottomed stainless steel bowl. Add egg yolks and mix well. Place the bowl over a hot water bath (barely simmering) and continue to beat until the yolks are thick and creamy. Be careful not to scramble the egg yolks; pull the bowl away from the hot water bath if it starts to get too hot.
Remove from heat. While whisking, gradually add the clarified butter to the egg yolks, drop by drop at first. If the sauce is too thick, thin with lemon juice or warm water.
Strain the sauce through cheesecloth. Season to taste with salt, cayenne and a little lemon juice. Add the remaining tarragon.
Hold warm for no longer than 1½ hours. Makes 1 pint.
To make Sauce Paloise, substitute fresh mint for the fresh tarragon. This is a good sauce for lamb.