Add the shallots, tarragon stems and half the leaves, peppercorns, and vinegar to a medium-size sauté pan.
Cook over low heat until the amount of liquid is reduced by three -fourths or about 1 tablespoon is left.
Transfer the mixture to a bowl over a double boiler over low heat.
Add the egg yolks to the bowl.
Whisk vigorously until it becomes thick and creamy, about 2 to 3 minutes.
Remove the bowl from the heat and slowly ladle in the clarified butter a few tablespoons at a time while vigorously whisking until the sauce becomes thick.
Strain the sauce through a chinois or a fine-mesh strainer.
Season with salt, cayenne, lemon-juice, parsley, and chopped tarragon, and mix until combined. Serve or hold for up to 90 minutes.
Notes
Make-Ahead: You can make this sauce up to 90 minutes ahead of time.How to Store: Cover and keep it in the refrigerator for up to 3 days.How to Reheat: Add the sauce back to a double boiler and whisk in a room temp egg yolk and a few tablespoons of hot water to help revive the sauce.If the sauce starts becoming too thick during or before adding in the clarified butter, whisk in a little bit of lemon juice or warm water.When whisking the egg yolks in the double boiler, take care to whisk vigorously or they will scramble. If they start to, you can save the sauce by immediately removing the bowl from the double-boiler.You may use less butter as it may thicken with less than the recipe calls for.