Slightly saute shallots in 1 tablespoon of the butter.
Add vinegar and wine on medium-low for 3 minutes. Reduce heat to low and continue to reduce for about 5 more minutes or until most of the liquid has evaporated.
In a separate pan, melt remaining butter until foamy. Pour into a measuring cup (with a spout) to slightly cool.
In a small mixing bowl, add the 3 egg YOLKS. Blend with an immersion blender just until lemon juice is incorporated.
Pour butter into egg/lemon mixture in a little at a time and blend with immersion blender until thick and creamy.
Blend in the shallot reduction and tarragon followed by the salt and pepper.; adjust taste, if needed. Refrigerate at least an hour before using to allow flavors to meld.
Spoon sauce on meat or vegetables. Refrigerate leftovers promptly.