In small saucepan, bring to a boil vinegar, water, 2 tablespoons chopped tarragon, the shallot. Boil until reduced to 2 tablespoons, 3 minutes. Strain; discard solids.
In blender, blend yolks, 1 tablespoon tarragon liquid, salt, cayenne until smooth and frothy. In small saucepan, heat butter until bubbly but not browned. With blender on high, slowly add half the butter, then remaining 1 tablespoon tarragon liquid. With blender running, add remaining butter until mixture is thickened. Add remaining chopped tarragon.
Press 1/2 teaspoon seasoning on each steak side. In skillet, heat oil over medium-high. Cook steaks 3 minutes per side for medium-rare (145°F). Serve with sauce.