Prepare the Reduction:

1. In a small saucepan, combine white wine, vinegar, chervil stems, tarragon stems, shallot slices, and black peppercorns.
2. Bring to a simmer over medium-high heat, then reduce heat to maintain a gentle simmer.
3. Cook until reduced to about 1 1/2 tablespoons, typically around 15 minutes.
4. Strain the reduction into a small bowl, ensuring to extract as much liquid as possible.

Make the Béarnaise Base:

1. In a blender or a container suitable for an immersion blender, combine the strained reduction, egg yolks, and a pinch of salt.
2. Melt the butter in a separate saucepan until foaming subsides, then transfer to a measuring cup.

Emulsify the Sauce:

1. With the blender running at medium speed, gradually add the hot melted butter to the egg yolk mixture, ensuring it emulsifies and becomes thick and creamy.
2. Season with salt to taste and mix again.

Final Touch:

1. Stir in the finely chopped tarragon and chervil by hand.
2. Serve immediately, or keep warm up to an hour before serving in a small lidded pan on very low heat. Whisk before serving.