Place the ingredients into a small saucepan, ensuring the tarragon is submerged into the liquid. Bring to the boil. Allow this liquid to reduce by more than half. Strain off the peppercorns and tarragon and allow the mixture to cool slightly.
Place the vinegar reduction in a large bowl with two egg yolks. Place this over a pot of simmering water. Whisk vigorously until the mixture becomes thick, pale and creamy. Remove the bowl from the heat now and slowly trickle the clarified butter into the yolk mixture, whisking continuously. Occasionally place the bowl back over the simmering water. The mixture should now be thick and glossy. Season well with salt and add fresh tarragon.
Season fillet well with salt and pepper and seal in a hot pan. Serve fillet rare with béarnaise sauce.