Combine wine, vinegar, tarragon, onion, and black pepper in a skillet; bring to a boil and cook until almost all the liquid is evaporated, 2 to 3 minutes.
Place butter in a microwave-safe bowl and heat in microwave until fully melted, 30 seconds to 1 minute.
Place tarragon mixture, egg yolks, lemon juice, salt, and cayenne pepper in a blender; pulse until combined, 5 to 10 seconds. Remove the small hole cover from lid; stream butter into egg mixture while blender is running until sauce is completely blended and smooth.
