Combine vinegar, wine, herb stems, shallots, and black peppercorns in a small saucepan. Bring to a simmer over medium-high heat and lower heat to maintain a gently simmer. Cook until reduced to about 1 1/2 tablespoons of liquid, about 15 minutes. Carefully strain liquid through a fine mesh strainer into a small bowl, pressing on the solids with the back of a spoon to extract as much liquid as possible.

Combine vinegar reduction, egg yolk, and a pinch of salt in the bottom of a jar that barely fits the head of an immersion blender. Melt butter for a minute in a microwave oven in a 1 cup measure with a pouring spout. The butter has to be hot not warm. This is the final step,do not microwave butter until all other components of recipe are ready, your backup water is boiling and you are prepared to serve.

Place head of immersion blender into the bottom of the jar and turn it on. With the blender constantly running, slowly but constantly pour hot butter into cup. While blending, move the immersion blender up and down, slowly, so to combine everything together, and to thicken. Continue pouring until all butter is added. This should only take about 30 seconds and the butter should emulsify with the egg yolk and vinegar reduction.  Sauce should be thick and creamy. 

If it is thin and runny, add 1 to 2 Tbs hot of boing water 1 Tbs at a time at a time while running blender until sauce is thickened. Season to taste with salt. Whisk in chopped tarragon and chervil. Serve immediately, or cover with plastic and transfer jar to a small pot of warm water and keep in a warm place for up to 15 minutes before serving. Béarnaise will solidify otherwise and cannot be reheated.